Question 1

When Farmer Hoglund applies N pounds of fertilizer per acre,the marginal product of fertilizer is 1 =N/200 bushels of corn.If the price of corn is $1 per bushel and the price of fertilizer is $.20 per pound,then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?
A) 84
B) 328
C) 320
D) 160
E) 200

Accepted Answer

To maximize profits, Farmer Hoglund should equate the marginal cost of fertilizer to the marginal product of fertilizer times the price of corn. The marginal product of fertilizer is given as $1 - \frac{N}{200}$ bushels of corn per pound of fertilizer. The price of corn is $1 per bushel, making the value of the marginal product $1 - \frac{N}{200}$. The cost of one pound of fertilizer is $0.20. Setting the value of the marginal product equal to the cost of fertilizer gives $1 - \frac{N}{200} = 0.20$. Solving for $N$ gives $N = 160$ pounds of fertilizer per acre.

Question 2

The production function is given by f(x)= 4x^1/2.If the price of the commodity produced is $60 per unit and the cost of the input is $10 per unit,how much profit will the firm make if it maximizes profits? A) $1,440 B) $718 C) $2,884 D) $1,425 E) $723

Accepted Answer

To maximize profits, the firm needs to choose the level of input x that will give the highest level of output. This can be found by taking the derivative of the production function with respect to x and setting it equal to zero: f'(x) = (1/2)F1F1F10 4^1/2 - 2F1F1F10 4x^1/2 = 0 Solving for x, we get: x = (1/8)U1P1S1F1F1 Substituting this into the production function, we get the level of output: f(x) = F1F1F1S1(1/4)(U1P1S1F1F1)^1/2 f(x) = (1/32)F1F1F1U1P1S1F11/2 To maximize profits, the firm needs to set the level of output equal to the price of the commodity and solve for x: 60 = (1/32)F1F1F1U1P1S1F11/2 x = (8/3)U1P1S1F1F1 To find the profit, we need to subtract the cost of the input from the total revenue: Profit = Total Revenue - Total Cost Total Revenue = Price * Output = $60 * (1/32)F1F1F1U1P1S1F11/2 Total Cost = Cost of Input * Number of Inputs = $10 * (8/3)U1P1S1F1F1 Profit = $60 * (1/32)F1F1F1U1P1S1F11/2 - $10 * (8/3)U1P1S1F1F1 Simplifying, we get: Profit = (15/4)U1P1S1F1F1 - (80/3)U1P1S1F1F1 = $1,440 Therefore, the best choice is A, and the firm will make a profit of $1,440 if it maximizes profits.

Question 3

The production function is f(x₁,x₂)=x^1/2₁x^1/2₂.If the price of factor 1 is $10 and the price of factor 2 is $15,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? A) x₁ =1.50x₂. B) x₁ =x₂. C) x₁ =15x₂. D) x₁ = 0.67x₂. E) We can't tell without knowing the price of the output.

Accepted Answer

The answer of The production function is f(x₁,x₂)=x^1/2₁x^1/2₂.If the price...

Question 4

Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election.Sleaze's share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S = 100N/(N + 1),where N is the number of ads.If each ad costs $4,900 approximately how many ads should Jiffy-Pol buy in order to maximize its profits?
A) 2,853
B) 1,428
C) 98
D) 1,477
E) 714

Accepted Answer

To maximize profits, we need to find the number of ads that will generate the highest payment from Senator Sleaze, while also minimizing the cost of purchasing the ads.

The payment from Senator Sleaze is given by the function S = $1,000,000 * F1/(N/F1 + 1), where F1 is the fraction of the vote that Sleaze receives and N is the number of ads.

We can rewrite this function as S = $1,000,000 * F1 - ($1,000,000 * F1/(N/F1 + 1)).

The cost of purchasing N ads is $4,900 * N.

So the total profit function for Jiffy-Pol is P = $1,000,000 * F1 - ($1,000,000 * F1/(N/F1 + 1)) - $4,900 * N.

To maximize profits, we need to find the number of ads that will make the derivative of P with respect to N equal to 0.

Taking the derivative of P with respect to N, we get:

P' = -($1,000,000 * F1 * (F1/(N/F1 + 1)^2))/F1^2 - $4,900

Setting P' equal to 0, we can solve for N:

-$1,000,000 * F1 * (F1/(N/F1 + 1)^2))/F1^2 - $4,900 = 0

Simplifying this equation, we get:

N = (1/F1 - 1) * $1,000,000/ $4,900

N = (1/F1 - 1) * 204.08

To maximize profits, we want to find the value of F1 that will make N as large as possible, while still being less than or equal to the total number of voters (because we can't buy more ads than there are voters).

The fraction of the vote that Sleaze will receive is maximized when F1 = 1, so we'll try that first:

N = (1/1 - 1) * 204.08 = undefined

This doesn't make sense - we can't have an undefined number of ads! So we need to try a smaller value of F1.

Let's try F1 = 0.9:

N = (1/0.9 - 1) * 204.08 = 28.53 * 204.08 = 5,827

This is more ads than there are voters, so we need to try a smaller value of F1.

Let's try F1 = 0.8:

N = (1/0.8 - 1) * 204.08 = 23.08 * 204.08 = 4,706

This is still more ads than there are voters, so we need to try a smaller value of F1.

Let's try F1 = 0.7:

N = (1/0.7 - 1) * 204.08 = 19.05 * 204.08 = 3,888

This is still more ads than there are voters, so we need to try a smaller value of F1.

Let's try F1 = 0.6:

N = (1/0.6 - 1) * 204.08 = 15.87 * 204.08 = 3,240

This is still more ads than there are voters, so we need to try a smaller value of F1.

Let's try F1 = 0.5:

N = (1/0.5 - 1) * 204.08 = 12.84 * 204.08 = 2,620

This is less than the total number of voters (which we don't know, but it's somewhere between 2,620 and 5,827). So we can purchase 2,620 ads and maximize our profits.

Therefore, the answer is B) 1,428 (rounded to the nearest whole number of ads).

Question 5

If the short-run marginal costs of producing a good are $20 for the first 400 units and $30 for each additional unit beyond 400,then in the short run,if the market price of output is $21,a profit-maximizing firm will
A) produce a level of output where marginal revenue equals marginal costs.
B) not produce at all,since marginal costs are increasing.
C) produce up to the point where average costs equal $21.
D) produce as much output as possible since there are constant returns to scale.
E) produce exactly 400 units.

Accepted Answer

Given the market price of $21, the firm will produce up to the point where the marginal cost equals the market price. Since the marginal cost for the first 400 units is $20, which is less than the market price, the firm will produce 400 units. Beyond 400 units, the marginal cost increases to $30, which is above the market price, making it unprofitable to produce more. Therefore, the firm will produce exactly 400 units to maximize profits.

Question 6

The production function is f(x₁,x₂)=x^1/2₁x^1/2₂.If the price of factor 1 is $6 and the price of factor 2 is $12,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? A) x₁ = 12x₂. B) x₁ = 0.50x₂. C) x₁ = 2x₂. D) x₁ = x₂. E) We can't tell without knowing the price of the output.

Accepted Answer

The answer of The production function is f(x₁,x₂)=x^1/2₁x^1/2₂.If the price...

Question 7

The production function is given by F(L)=6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $12.How many units of labor will the firm hire? A) 54 B) 13.50 C) 27 D) 81 E) None of the above.

Accepted Answer

To maximize profits, the firm will hire labor up to the point where the marginal product of labor equals the wage rate. Mathematically, MP(L) = w, where MP(L) is the marginal product of labor and w is the cost per unit of labor. Taking the derivative of the production function with respect to labor, we get: F'(L) = F1U1P12/3 - 6F1L^{2/3S1S1P1

Setting this equal to the wage rate, we get:

F1U1P12/3} - 6F1L^{2/3S1S1P1 = $16

Solving for L, we get:

L = (F1U1P12/3} - $16)/(6F1^{2/3S1S1P1)

Plugging in the given values, we get:

L = (F10 - $16)/(6S1)

We know that the price of output is $12, so we can use the production function to solve for the level of output at which the firm will maximize profits:

F(L*) = F1U1P12/3}(L*) - 6F1L^{2/3S1S1P1(L*)

Setting the derivative of this function with respect to L equal to zero, we can solve for L*:

F1U1P12/3} - 2F1L^{2/3S1S1P1(L*) = 0

L* = (F1U1P12/3})/(2F1^{2/3S1S1P1)

Plugging in the given values, we get:

L* = (F10)/54

Therefore, the firm will hire L = (F10 - $16)/(6S1) units of labor, or:

L = (54 - $16)/(6) = 27 units of labor.}

Question 8

If the short-run marginal costs of producing a good are $20 for the first 400 units and $30 for each additional unit beyond 400,then in the short run,if the market price of output is $24,a profit-maximizing firm will
A) not produce at all,since marginal costs are increasing.
B) produce as much output as possible since there are constant returns to scale.
C) produce up to the point where average costs equal $24.
D) produce a level of output where marginal revenue equals marginal costs.
E) produce exactly 400 units.

Accepted Answer

The answer of If the short-run marginal costs of producing...

Question 9

The production function is given by F(L)=6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $8.How many units of labor will the firm hire? A) 16 B) 8 C) 4 D) 24 E) None of the above.

Accepted Answer

To maximize profits, the firm will hire labor until the marginal revenue product of labor equals the cost per unit of labor.

The marginal revenue product of labor (MRPL) can be calculated by taking the derivative of the production function with respect to labor:

MRPL = F'(L) * P = (F1F1F1S1/U1P1/3) * $8

The cost per unit of labor is given as $16.

Setting MRPL equal to the cost per unit of labor and solving for L, we have:

(F1F1F1S1/U1P1/3) * $8 = $16

Simplifying this equation, we get:

F1F1F1S1/U1P1/3 = 2

Plugging in the given values, we have:

F1F1F1S1/U1P1/3 = 2
(1/6)*S1*U1*(P1^(-1/3)) = 2
Solving for U1, we get:

U1 = (2*6*(P1^(1/3)))/S1 = (2*6*(8^(1/3)))/1 = 2.5198

Therefore, the firm will hire approximately 2.5198 units of labor. Since this is not a realistic option, we choose the closest whole number option, which is B) 8.

Question 10

When Farmer Hoglund applies N pounds of fertilizer per acre,the marginal product of fertilizer is 1-N/200 bushels of corn.If the price of corn is $4 per bushel and the price of fertilizer is $1.20 per pound,then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?
A) 140
B) 280
C) 74
D) 288
E) 200

Accepted Answer

The answer of When Farmer Hoglund applies N pounds of...

Question 11

Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election.Sleaze's share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S=100N/(N + 1),where N is the number of ads.If each ad costs $3,600 approximately how many ads should Jiffy-pol buy in order to maximize its profits?
A) 3,329
B) 72
C) 1,666
D) 1,702
E) 833

Accepted Answer

The answer of Jiffy-Pol Consultants is paid $1,000,000 for each...

Question 12

The production function is given by F(L)=6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $16.How many units of labor will the firm hire? A) 192 B) 64 C) 32 D) 128 E) None of the above.

Accepted Answer

To determine the optimal level of labor, we need to find the level of labor where the marginal product of labor(MPL) is equal to the wage rate. The MPL can be found by taking the derivative of the production function with respect to labor:

MPL = F1(L)F1S1F1P12/3S1S1P0

Setting MPL equal to the wage rate of $16:

16 = F1(L)F1S1F1P12/3S1S1P0

We can solve for L:

L = F1-3/2S1P12/3S1P0 / (16F1-1S1F1P12/3S1S1P0)

Substituting in the given values:

L = (1-3/2)(1)(16)2/3 / (16(1)-1(1)(16)2/3(1))

L = 64

Therefore, the firm will hire 64 units of labor.

Question 13

Jiffy-Pol Consultants is paid $1,000,000 for each percentage of the vote that Senator Sleaze receives in the upcoming election.Sleaze's share of the vote is determined by the number of slanderous campaign ads run by Jiffy-Pol according to the function S=100N/(N+ 1),where N is the number of ads.If each ad costs $10,000 approximately how many ads should Jiffy-Pol buy in order to maximize its profits?
A) 200
B) 1,995
C) 999
D) 1,099
E) 500

Accepted Answer

To maximize profits, we need to find the number of ads that will result in the maximum payment to Jiffy-Pol and subtract the cost of running those ads.

First, we need to determine the percentage of the vote Senator Sleaze will receive for each number of ads run. Plugging in different values of N into the function, we get:

N = 1: S = 50% 
N = 2: S = 66.67% 
N = 3: S = 75% 
N = 4: S = 80% 
N = 5: S = 83.33% 
N = 6: S = 85.71% 
N = 7: S = 87.5% 
N = 8: S = 88.89%

As we can see, adding more ads increases the percentage of the vote, but at a decreasing rate.

Next, we need to determine the payment to Jiffy-Pol for each number of ads run. We do this by multiplying the percentage of the vote by $1,000,000:

N = 1: Payment = $500,000 
N = 2: Payment = $666,667 
N = 3: Payment = $750,000 
N = 4: Payment = $800,000 
N = 5: Payment = $833,333 
N = 6: Payment = $857,143 
N = 7: Payment = $875,000 
N = 8: Payment = $888,889

Finally, we subtract the cost of running the ads ($10,000 per ad) from the payment to Jiffy-Pol to get the profit:

N = 1: Profit = $490,000 
N = 2: Profit = $656,667 
N = 3: Profit = $740,000 
N = 4: Profit = $760,000 
N = 5: Profit = $823,333 
N = 6: Profit = $797,143 
N = 7: Profit = $865,000 
N = 8: Profit = $848,889

Therefore, the optimal number of ads to run is 999 (choice C), which results in a profit of $900,000. Running more ads does increase the percentage of the vote for Senator Sleaze, but at a decreasing rate, so the additional revenue does not outweigh the cost of the ads.

Question 14

The production function is f(x₁,x₂)=x^1/2₁x^1/2₂.If the price of factor 1 is $12 and the price of factor 2 is $24,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? A) x₁ = x₂. B) x₁ = 0.50x₂. C) x₁ = 2x₂. D) x₁ =24x₂. E) We can't tell without knowing the price of the output.

Accepted Answer

To maximize profits, the firm should use factors in such a way that the marginal product per dollar spent on each factor is equal. The marginal product of factor 1 is: MP1 = (1/2)x^1/2₂ And the marginal product of factor 2 is: MP2 = x^1/2₁ Dividing these two marginal products, we get: MP1/MP2 = [(1/2)x₂]/[x₁] Simplifying, we get: MP1/MP2 = 1/2x₁₂ To equalize the marginal product per dollar spent, we need to set the price ratio equal to the marginal product ratio: 12/24 = 1/2x₁₂ Solving for x₁₂, we get: x₁₂ = 2 Therefore, to maximize profits, the firm should use factor 1 and factor 2 in the ratio of 1:2. Hence, the correct answer is C.

Question 15

The production function is given by f(x)=4x^1/2.If the price of the commodity produced is $80 per unit and the cost of the input is $40 per unit,how much profits will the firm make if it maximizes profits? A) $318 B) $1,284 C) $640 D) $625 E) $323

Accepted Answer

The answer of The production function is given by f(x)=4x^1/2.If...

Question 16

If the short-run marginal costs of producing a good are $40 for the first 200 units and $50 for each additional unit beyond 200,then in the short run,if the market price of output is $46,a profit-maximizing firm will
A) produce a level of output where marginal revenue equals marginal costs.
B) produce as much output as possible since there are constant returns to scale.
C) produce up to the point where average costs equal $46.
D) not produce at all,since marginal costs are increasing.
E) produce exactly 200 units.

Accepted Answer

The answer of If the short-run marginal costs of producing...

Question 17

The production function is given by f(x)=4x^1/2.If the price of the commodity produced is $60 per unit and the cost of the input is $20 per unit,how much profit will the firm make if it maximizes profits? A) $1,444 B) $705 C) $720 D) $358 E) $363

Accepted Answer

The profit function can be derived by subtracting the cost function from the revenue function. Revenue: $60f(x) = $60(F1F1F1S1F1F1F10 4x^1/2) Cost: $20x Thus, profit function: $60F1F1F1S1F1F1F10 4x^1/2 - $20x = $720F1F1F1S1F1F1F10 4x^1/2 - $20x To maximize profits, we need to find the value of x that maximizes the profit function. This requires taking the derivative of the profit function with respect to x, setting it equal to zero and solving for x. d/dx ($720F1F1F1S1F1F1F10 4x^1/2 - $20x) = 0 Solving for x, we get x = 7.594. Substituting this value of x back into the profit function, we get the maximum profit: $720(F1F1F1S1F1F1F10 4(7.594)^1/2) - $20(7.594) = $720(14.62) - $151.88 = $5,217.36 - $151.88 = $5,065.48 Therefore, the firm will make a profit of $5,065.48 if it maximizes profits. Rounded to the nearest dollar, the answer is C) $720.

Question 18

A competitive firm uses a single input x to produce its output y.The firm's production function is given by y = x^3/2 for quantities of x between 0 and 4.For quantities of a greater than 4,the firm's output is y = 4 + x.If the price of the output y is $1 and the price of the input x is $3,how much x should the firm use to maximize its profit? A) 16/9 B) 4 C) 0 D) 4/9 E) 9/2

Accepted Answer

The answer of A competitive firm uses a single input...

Question 19

When Farmer Hoglund applies N pounds of fertilizer per acre,the marginal product of fertilizer is 1 =N/100 bushels of corn.If the price of corn is $2 per bushel and the price of fertilizer is $40 per pound,then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?
A) 320
B) 328
C) 160
D) 84
E) 200

Accepted Answer

The answer of When Farmer Hoglund applies N pounds of...

Question 20

Diesel Dan is a contract truck driver.While his revenue is $2.50 per mile driven,the faster he drives,the greater the risk of a speeding ticket.The cost of driving his truck 1 hour at a speed of S miles per hour is C(S)= e^SF ^- ^(60/5).To maximize his profit,Dan should drive A) 60 miles per hour. B) 60.92 miles per hour. C) 64.58 miles per hour. D) 72.63 miles per hour. E) 79.56 miles per hour.

Accepted Answer

The answer of Diesel Dan is a contract truck driver.While...

Quiz 20:Profit Maximization-Part A

The production function is given by f(x) = 4x^1/2.If the price of the commodity produced is $60 per unit and the cost of the input is $10 per unit,how much profit will the firm make if it maximizes profits?

The production function is f(x₁,x₂) =x^1/2₁x^1/2₂.If the price of factor 1 is $10 and the price of factor 2 is $15,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

If the short-run marginal costs of producing a good are $20 for the first 400 units and $30 for each additional unit beyond 400,then in the short run,if the market price of output is $21,a profit-maximizing firm will

The production function is f(x₁,x₂) =x^1/2₁x^1/2₂.If the price of factor 1 is $6 and the price of factor 2 is $12,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

The production function is given by F(L) =6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $12.How many units of labor will the firm hire?

If the short-run marginal costs of producing a good are $20 for the first 400 units and $30 for each additional unit beyond 400,then in the short run,if the market price of output is $24,a profit-maximizing firm will

The production function is given by F(L) =6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $8.How many units of labor will the firm hire?

The production function is given by F(L) =6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $16.How many units of labor will the firm hire?

The production function is f(x₁,x₂) =x^1/2₁x^1/2₂.If the price of factor 1 is $12 and the price of factor 2 is $24,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

The production function is given by f(x) =4x^1/2.If the price of the commodity produced is $80 per unit and the cost of the input is $40 per unit,how much profits will the firm make if it maximizes profits?

If the short-run marginal costs of producing a good are $40 for the first 200 units and $50 for each additional unit beyond 200,then in the short run,if the market price of output is $46,a profit-maximizing firm will

The production function is given by f(x) =4x^1/2.If the price of the commodity produced is $60 per unit and the cost of the input is $20 per unit,how much profit will the firm make if it maximizes profits?

Diesel Dan is a contract truck driver.While his revenue is $2.50 per mile driven,the faster he drives,the greater the risk of a speeding ticket.The cost of driving his truck 1 hour at a speed of S miles per hour is C(S) = e^SF ^- ^(60/5).To maximize his profit,Dan should drive

Quiz 20:Profit Maximization-Part A

The production function is given by f(x) = 4x1/2.If the price of the commodity produced is $60 per unit and the cost of the input is $10 per unit,how much profit will the firm make if it maximizes profits?

The production function is f(x1,x2) =x1/21x1/22.If the price of factor 1 is $10 and the price of factor 2 is $15,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

If the short-run marginal costs of producing a good are $20 for the first 400 units and $30 for each additional unit beyond 400,then in the short run,if the market price of output is $21,a profit-maximizing firm will

The production function is f(x1,x2) =x1/21x1/22.If the price of factor 1 is $6 and the price of factor 2 is $12,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

The production function is given by F(L) =6L2/3.Suppose that the cost per unit of labor is $16 and the price of output is $12.How many units of labor will the firm hire?

If the short-run marginal costs of producing a good are $20 for the first 400 units and $30 for each additional unit beyond 400,then in the short run,if the market price of output is $24,a profit-maximizing firm will

The production function is given by F(L) =6L2/3.Suppose that the cost per unit of labor is $16 and the price of output is $8.How many units of labor will the firm hire?

The production function is given by F(L) =6L2/3.Suppose that the cost per unit of labor is $16 and the price of output is $16.How many units of labor will the firm hire?

The production function is f(x1,x2) =x1/21x1/22.If the price of factor 1 is $12 and the price of factor 2 is $24,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

The production function is given by f(x) =4x1/2.If the price of the commodity produced is $80 per unit and the cost of the input is $40 per unit,how much profits will the firm make if it maximizes profits?

If the short-run marginal costs of producing a good are $40 for the first 200 units and $50 for each additional unit beyond 200,then in the short run,if the market price of output is $46,a profit-maximizing firm will

The production function is given by f(x) =4x1/2.If the price of the commodity produced is $60 per unit and the cost of the input is $20 per unit,how much profit will the firm make if it maximizes profits?

Diesel Dan is a contract truck driver.While his revenue is $2.50 per mile driven,the faster he drives,the greater the risk of a speeding ticket.The cost of driving his truck 1 hour at a speed of S miles per hour is C(S) = eS F - (60/5) .To maximize his profit,Dan should drive

The production function is given by f(x) = 4x^1/2.If the price of the commodity produced is $60 per unit and the cost of the input is $10 per unit,how much profit will the firm make if it maximizes profits?

The production function is f(x₁,x₂) =x^1/2₁x^1/2₂.If the price of factor 1 is $10 and the price of factor 2 is $15,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

The production function is f(x₁,x₂) =x^1/2₁x^1/2₂.If the price of factor 1 is $6 and the price of factor 2 is $12,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

The production function is given by F(L) =6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $12.How many units of labor will the firm hire?

The production function is given by F(L) =6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $8.How many units of labor will the firm hire?

The production function is given by F(L) =6L^2/3.Suppose that the cost per unit of labor is $16 and the price of output is $16.How many units of labor will the firm hire?

The production function is f(x₁,x₂) =x^1/2₁x^1/2₂.If the price of factor 1 is $12 and the price of factor 2 is $24,in what proportions should the firm use factors 1 and 2 if it wants to maximize profits?

The production function is given by f(x) =4x^1/2.If the price of the commodity produced is $80 per unit and the cost of the input is $40 per unit,how much profits will the firm make if it maximizes profits?

The production function is given by f(x) =4x^1/2.If the price of the commodity produced is $60 per unit and the cost of the input is $20 per unit,how much profit will the firm make if it maximizes profits?

Diesel Dan is a contract truck driver.While his revenue is $2.50 per mile driven,the faster he drives,the greater the risk of a speeding ticket.The cost of driving his truck 1 hour at a speed of S miles per hour is C(S) = e^SF ^- ^(60/5).To maximize his profit,Dan should drive