Question 1

Suppose that  tons is the production function for a product with x units of one input and y units of a second input. Find the values of x and y that will maximize production. ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Suppose that  tons is the production...

Question 2

A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are ​  ​
Find the number of each type of product that should be manufactured to maximize profit.
​
A)3,000 units of product A 48,000 units of product B
B)6,000 units of product A 24,000 units of product B
C)12,000 units of product A 12,000 units of product B
D)3,000 units of product A 12,000 units of product B
E)12,000 units of product A 48,000 units of product B

Accepted Answer

The answer of A company manufactures two products, A and...

Question 3

Suppose that the following table shows the average hourly earnings for full-time production workers in various industries for selected years. Find the linear regression equation for hourly earnings as a function of time (with  representing 1970). Round numerical values in your answer to four decimal places. ​  ​
A) 
(where 
Is the number of years after 1970 and 
Is the average hourly wage)
B) 
(where 
Is the number of years after 1970 and 
Is the average hourly wage)
C) 
(where 
Is the number of years after 1970 and 
Is the average hourly wage)
D) 
(where 
Is the number of years after 1970 and 
Is the average hourly wage)
E) 
(where 
Is the number of years after 1970 and 
Is the average hourly wage)

Accepted Answer

The answer of Suppose that the following table shows the...

Question 4

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980. ​ 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of The following table shows the median age...

Question 5

Test for relative maximum and minimum. ​  ​
A)relative maxima when x = 7, y = -8 and x = 7, y = 8; relative minima when x = -7, y = 8 and x = -7, y = -8
B)relative maximum when x = 7, y = -8; relative minimum when x = -7, y = 8
C)saddle point when x = -7, y = -8; relative minima when x = 0, y = 0 and x = -7, y = -8
D)saddle points when x = 7, y = -8 and x = -7, y = 8; relative maximum when x = -7, y = -8; relative minimum when x = 7, y = 8
E)saddle points when x = 7, y = 8 and x = -7, y = -8; relative maxima when x = 7, y = -8 and x = -7, y = 8

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 6

Test for relative maximum and minimum. ​  ​
A)relative maximum at 
B)saddle point at 
C)relative maximum at 
D)relative minimum at 
E)saddle point at

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 7

Test for relative maximum and minimum. ​  ​
A)relative maximum at 
B)relative maximum at 
C)relative minimum at 
D)relative minimum at 
E)relative minimum at

Accepted Answer

The given function has a relative minimum at the point (11eb0d3b_98b9_ff74_9790_2bfb13ac3835_TB1243_11) because the function's value is lower at that point than at surrounding points in its immediate vicinity.

Question 8

Suppose that x units of one input and y units of a second input result in  units of a product. What is the maximum production? ​
A)1,675
B)​3,081
C)​1,152
D)​1,027
E)​1,425

Accepted Answer

The answer of Suppose that x units of one input...

Question 9

Suppose that the following table shows the average hourly earnings for full-time production workers in various industries for selected years. The linear regression equation for hourly earnings as a function of time is given by  (where x is the number of years after 1970 and y is the average hourly wage). What does this model predict for the average hourly earnings in 2024? Round your answer to two decimal places. ​ 
A)$42.51
B)$327.10
C)$43.41
D)$326.20
E)$325.80

Accepted Answer

The answer of Suppose that the following table shows the...

Question 10

Test for relative maximum and minimum. ​  ​
A)relative minimum at 
And saddle point at 
B)relative maximum at 
And saddle point at 
C)relative minimum at 
D)relative maximum at 
E)saddle points at 
And

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 11

Test for relative maximum and minimum. ​  ​
A)relative minimum at 
B)relative maximum at 
C)saddle point at 
D)relative maximum at 
E)relative minimum at

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 12

Test for relative maximum and minimum. ​  ​
A)saddle point at 
B)saddle point at 
C)saddle point at 
D)relative minimum at 
E)relative minimum at

Accepted Answer

The answer of Test for relative maximum and minimum. ​...

Question 13

Suppose that a manufacturer produces two brands of a product, brand 1 and brand 2. Suppose the demand for brand 1 is thousand units and the demand for brand 2 is thousand units, where p₁ and p₂ prices in dollars. If the joint cost function is , in thousands of dollars, how many of each brand should be produced to maximize profit? A)74 units of brand 1 82 units of brand 2 B)9 units of brand 1 52 units of brand 2 C)74 units of brand 1 52 units of brand 2 D)14 units of brand 1 38 units of brand 2 E)27 units of brand 1 77 units of brand 2

Accepted Answer

The answer of Suppose that a manufacturer produces two brands...

Question 14

Test  for relative maximum and minimum. ​
A)The point 
Is a saddle point.A relative maximum occurs at 
)
B)The point 
Is a saddle point.A relative maximum occurs at 
)
C)The point 
Is a saddle point.A relative maximum occurs at 
)
D)The point 
Is a saddle point.A relative minimum occurs at 
)
E)The point 
Is a saddle point.A relative minimum occurs at 
)

Accepted Answer

The answer of Test  for relative maximum and minimum....

Question 15

Find the values for each of the dimensions of an open-top box of length x, width y, and height  (in inches) such that the box requires the least amount of material to make. ​
A)length = 8 inches width = 8 inches
Height = 4 inches
B)length = 4 inches width = 8 inches
Height = 8 inches
C)length = 8 inches width = 4 inches
Height = 8 inches
D)length = 4 inches width = 4 inches
Height = 16 inches
E)length = 16 inches width = 4 inches
Height = 4 inches

Accepted Answer

The answer of Find the values for each of the...

Question 16

Find x and y such that  subject to the condition  attains a minimum value. ​
A) 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

To find the values of x and y that minimize the given expression, we need to solve for the roots of the equation:

11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 = (x + y + 1)^2 + (x - y - 1)^2

Expanding the equation, we get:

11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 = 2(x^2 + y^2 + 1) + 2

Simplifying further, we get:

(x^2 + y^2) = (1/2) * (11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 - 2)

Since we want to minimize the expression, we want to find the smallest value of (x^2 + y^2) that satisfies this equation. The smallest value of the right-hand side is achieved when 11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 is minimized, which occurs when x = 0 and y = 0. Substituting these values, we get:

(x^2 + y^2) = 0.5 * (11eb0d3b_98bc_97e1_9790_655b61572ad5_TB1243_11 - 2) = 0.5 * 11eb0d3b_98bc_97e0_9790_330a0c6e9027_TB1243_11

Thus, the minimum value is achieved when x = 0 and y = 0, and the answer is choice C, 11eb0d3b_98bc_97e4_9790_49e29a8a1396_TB1243_11.

Question 17

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by  , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight? ​
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A new food is designed to add...

Question 18

Suppose that the profit from the sale of Kandy and Kreams is given by  dollars, where x is the number of pounds of Kandy and y is the number of pounds of Kreams. How many pounds of Kandy and Kreams must be sold to maximize profit? What is the maximum profit? Round your pounds answers to the nearest whole number. Round your max profit answer to the nearest cent. ​
A)40 pounds of Kandy, 200 pounds of Kreams, max profit of $661.00
B)6 pounds of Kandy, 15 pounds of Kreams, max profit of $477.45
C)12 pounds of Kandy, 30 pounds of Kreams, max profit of $865.80
D)20 pounds of Kandy, 100 pounds of Kreams, max profit of $1,620.00
E)60 pounds of Kandy, 300 pounds of Kreams, max profit of $315.34

Accepted Answer

To find the maximum profit, we need to find the critical points of the profit function.

Profit function: P(x,y) = 11eb0d3b_98bb_110e_9790_afc3e21faffa_TB1243_11

We can use partial derivatives to find the critical points:

∂P/∂x = 110e^(-0.01x-0.02y) - 28 = 0
∂P/∂y = 220e^(-0.01x-0.02y) - 35 = 0

Solving for x and y, we get:

x = 200
y = 100

To verify that it is a maximum, we check the second partial derivatives:

∂^2P/∂x^2 = -1100e^(-0.01x-0.02y) < 0 (at x = 200, y = 100)
∂^2P/∂y^2 = -4400e^(-0.01x-0.02y) < 0 (at x = 200, y = 100)
∂^2P/∂x∂y = -2200e^(-0.01x-0.02y) < 0 (at x = 200, y = 100)

Since the second partial derivatives are negative, we know that it is a maximum. Therefore, to maximize profit, 20 pounds of Kandy and 100 pounds of Kreams should be sold, resulting in a maximum profit of $1,620.00.

Question 19

The following table gives the actual or projected population in millions for a certain city for selected years from 2000 to 2050. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 2000. ​ 
A) 
B)​ 
C)​ 
D)​ 
E)​

Accepted Answer

The answer of The following table gives the actual or...

Question 20

Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make. ​
A)x = 46 inches, y = 46 inches, z = 46 inches
B)x = 32 inches, y = 32 inches, z = 32 inches
C)x = 41 inches, y = 41 inches, z = 41 inches
D)x = 45 inches, y = 45 inches, z = 45 inches
E)x = 34 inches, y = 34 inches, z = 34 inches

Accepted Answer

The box that requires the least amount of material for a given volume is a cube. The volume of a cube is given by V = s^3, where s is the side length. Solving 32,768 = s^3 gives s = 32, so the dimensions are 32 inches by 32 inches by 32 inches.

Quiz 15: Functions of Two or More Variables

Suppose that tons is the production function for a product with x units of one input and y units of a second input. Find the values of x and y that will maximize production.

A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are Find the number of each type of product that should be manufactured to maximize profit.

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Suppose that x units of one input and y units of a second input result in units of a product. What is the maximum production?

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Find the values for each of the dimensions of an open-top box of length x, width y, and height (in inches) such that the box requires the least amount of material to make.

Find x and y such that subject to the condition attains a minimum value.

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight?

The following table gives the actual or projected population in millions for a certain city for selected years from 2000 to 2050. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 2000.

Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make.

Quiz 15: Functions of Two or More Variables

Suppose that tons is the production function for a product with x units of one input and y units of a second input. Find the values of x and y that will maximize production. ​

A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are ​ ​ Find the number of each type of product that should be manufactured to maximize profit. ​

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980. ​

Test for relative maximum and minimum. ​ ​

Test for relative maximum and minimum. ​ ​

Test for relative maximum and minimum. ​ ​

Suppose that x units of one input and y units of a second input result in units of a product. What is the maximum production? ​

Test for relative maximum and minimum. ​ ​

Test for relative maximum and minimum. ​ ​

Test for relative maximum and minimum. ​ ​

Test for relative maximum and minimum. ​

Find the values for each of the dimensions of an open-top box of length x, width y, and height (in inches) such that the box requires the least amount of material to make. ​

Find x and y such that subject to the condition attains a minimum value. ​

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight? ​

The following table gives the actual or projected population in millions for a certain city for selected years from 2000 to 2050. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 2000. ​

Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make. ​

Suppose that tons is the production function for a product with x units of one input and y units of a second input. Find the values of x and y that will maximize production.

A company manufactures two products, A and B. If x is the number of thousands of units of A and y is the number of thousands of units of B, then the cost and revenue in thousands of dollars are Find the number of each type of product that should be manufactured to maximize profit.

The following table shows the median age of automobiles and trucks on the road for a certain country. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 1980.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Suppose that x units of one input and y units of a second input result in units of a product. What is the maximum production?

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Test for relative maximum and minimum.

Find the values for each of the dimensions of an open-top box of length x, width y, and height (in inches) such that the box requires the least amount of material to make.

Find x and y such that subject to the condition attains a minimum value.

A new food is designed to add weight to mature beef cattle. The weight in pounds is given by , where x is the number of units of the first ingredient and y is the number of units of the second ingredient. How many units of each ingredient will maximize the weight?

The following table gives the actual or projected population in millions for a certain city for selected years from 2000 to 2050. Use linear regression to find the linear equation that is the best fit for the data, with x equal to the number of years past 2000.

Find the values for each of the dimensions of a closed-top box of length x, width y, and height z (in inches) if the volume equals 32,768 cubic inches and the box requires the least amount of material to make.