Question 1

A rectangular closed box with a square base is to have a volume of 1000  
.Find its dimensions if the box is to require the least possible material.

Accepted Answer

The answer of A rectangular closed box with a square...

Question 2

A rectangular plot adjacent to a stream is to be fenced in by using the stream as one side of the enclosed area.If 2000 ft of fencing are to be used,find the maximum area that can be enclosed.Assume the answer is in square feet.

Accepted Answer

The answer of A rectangular plot adjacent to a stream...

Question 3

A manufacturer has to produce annually 360 units of a product that are sold at a uniform rate during the year.The production cost for each unit is $200,and carrying costs (insurance,interest,storage,and so on)are estimated to be 10% of the value of average inventory.Set-up costs per production run are $100.Find the economic lot size.

Accepted Answer

The answer of A manufacturer has to produce annually 360...

Question 4

A cable TV company has 500 customers paying $20 each month.For each $1 reduction in price,the company attracts 50 more customers.Find the price that yields maximum revenue.

Accepted Answer

The answer of A cable TV company has 500 customers...

Question 5

A company owns an apartment building containing 100 units.If the company charges $400 per month rent,then all units can be rented out,and for every increase of $20 per month in rent,the company will lose one customer.What rent should be charged to maximize revenue?

Accepted Answer

The answer of A company owns an apartment building containing...

Question 6

A manufacturer has to produce annually 1000 units of a product that are sold at a uniform rate during the year.The production cost for each unit is $400,and carrying costs (insurance,interest,storage,and so on)are estimated to be 5% of the value of average inventory.Set-up costs per production run are $64.Find the economic lot size.

Accepted Answer

The answer of A manufacturer has to produce annually 1000...

Question 7

An open box is to be made by cutting equal squares from each corner of a 20-in.square piece of cardboard and then folding up the sides.Find the length of the side of the square that must be cut out if the volume of the box is to be maximized.

Accepted Answer

The answer of An open box is to be made...

Question 8

The demand equation for a monopolist's product is p =  ,where p is the price per unit (in dollars)for q units.If the total cost c (in dollars)of producing q units is given by c = 5q+ 2000,then the level of production at which profit is maximized is

Accepted Answer

The answer of The demand equation for a monopolist's product...

Question 9

Using fencing,a rectangular area is to be enclosed next to the wall of a building.The building will form one of the sides and no fencing will be placed there.The cost of the fencing for the side opposite the building is $5 per foot.The cost of the fencing for the other two sides is $3 per foot.The area to be enclosed is 3000  
.In order to keep expenses of the three sides to a minimum,how many feet of each type of fencing must be bought?

Accepted Answer

The answer of Using fencing,a rectangular area is to be...

Question 10

A rectangular plot of ground is to be fenced in so that it has an area of 15,000 square feet.The plot is to be divided in half with a fence parallel to one pair of sides.Find the dimensions of the plot if the least amount of fencing is to be used.

Accepted Answer

The answer of A rectangular plot of ground is to...

Question 11

You have been asked to design a rectangular box with a square base and lid.The volume of the box must be  The cost per square foot of material for the base is $0.50,for the sides $0.20,and for the lid $0.10.If the total cost of materials is a minimum,then the dimensions (in feet)of the box are

Accepted Answer

The answer of You have been asked to design a...

Question 12

Sensitivity to a drug depends on the dosage size x according to the equation s = 50x -  
.Find the dosage that maximizes sensitivity.

Accepted Answer

The answer of Sensitivity to a drug depends on the...

Question 13

It is estimated that under a short-term energy-assistance plan,n million households will receive direct aid in meeting home-fuel costs after t years,where  
For what value of t will n be a maximum?

Accepted Answer

The answer of It is estimated that under a short-term...

Question 14

It is estimated that under a short-term energy-assistance plan,n million households will receive direct aid in meeting home-fuel costs after t years,where n = 2  
- 15  
+ 36t,0 ≤ t ≤ 3.For what value of t will n be a maximum?

Accepted Answer

The answer of It is estimated that under a short-term...

Question 15

A real estate firm owns 70 apartments.At $200 per month each apartment can be rented.However,for each $10 per month increase,there will be two vacancies with no possibility of filling them.What rent per apartment will maximize monthly revenue?

Accepted Answer

The answer of A real estate firm owns 70 apartments.At...

Question 16

The demand function for a monopolist's product is p = 100 - 3q,where p is the price per unit (in dollars)for q units.If the average cost  
(in dollars)per unit for q units is  
= 4 +  
,find the output q at which profit is maximized.

Accepted Answer

The answer of The demand function for a monopolist's product...

Question 17

An open box is to have a surface area of 300  
.The base of the box is to be a square.Find the dimensions of the box that maximize volume.

Accepted Answer

The answer of An open box is to have a...

Question 18

A cable TV company has 200 customers paying $10 each month.For each $1 reduction in price,the company attracts 50 more customers.Find the price that yields maximum revenue.

Accepted Answer

The answer of A cable TV company has 200 customers...

Question 19

A manufacturer has determined that the total cost c of producing q units of a product is given by  Average cost will be a minimum at a production level of

Accepted Answer

To find the minimum average cost, we need to find the derivative of the cost function with respect to q and set it equal to zero.

c = 1500 + 6q + 0.01q^2

Taking the derivative with respect to q:

c' = 6 + 0.02q

Setting c' equal to zero and solving for q:

6 + 0.02q = 0 
0.02q = -6 
q = -300

Since a negative production level doesn't make sense, we reject this solution. The only other critical point is a minimum at q = 300, but we need to check if it's indeed a minimum.

Taking the second derivative:

c'' = 0.02

Since c'' is positive, we have a minimum at q = 300. Therefore, the best choice is C, 400 units.

Question 20

A company owns an apartment building containing 80 units.If the company charges $300 per month rent,then all units can be rented out,and for every increase of $10 per month in rent,the company will lose one customer.What rent should be charged to maximize revenue?

Accepted Answer

The answer of A company owns an apartment building containing...

Quiz 14: Curve Sketching

A rectangular closed box with a square base is to have a volume of 1000 .Find its dimensions if the box is to require the least possible material.

A rectangular plot adjacent to a stream is to be fenced in by using the stream as one side of the enclosed area.If 2000 ft of fencing are to be used,find the maximum area that can be enclosed.Assume the answer is in square feet.

A cable TV company has 500 customers paying $20 each month.For each $1 reduction in price,the company attracts 50 more customers.Find the price that yields maximum revenue.

A company owns an apartment building containing 100 units.If the company charges $400 per month rent,then all units can be rented out,and for every increase of $20 per month in rent,the company will lose one customer.What rent should be charged to maximize revenue?

An open box is to be made by cutting equal squares from each corner of a 20-in.square piece of cardboard and then folding up the sides.Find the length of the side of the square that must be cut out if the volume of the box is to be maximized.

The demand equation for a monopolist's product is p = ,where p is the price per unit (in dollars) for q units.If the total cost c (in dollars) of producing q units is given by c = 5q+ 2000,then the level of production at which profit is maximized is

A rectangular plot of ground is to be fenced in so that it has an area of 15,000 square feet.The plot is to be divided in half with a fence parallel to one pair of sides.Find the dimensions of the plot if the least amount of fencing is to be used.

You have been asked to design a rectangular box with a square base and lid.The volume of the box must be The cost per square foot of material for the base is $0.50,for the sides $0.20,and for the lid $0.10.If the total cost of materials is a minimum,then the dimensions (in feet) of the box are

Sensitivity to a drug depends on the dosage size x according to the equation s = 50x - .Find the dosage that maximizes sensitivity.

It is estimated that under a short-term energy-assistance plan,n million households will receive direct aid in meeting home-fuel costs after t years,where For what value of t will n be a maximum?

It is estimated that under a short-term energy-assistance plan,n million households will receive direct aid in meeting home-fuel costs after t years,where n = 2 - 15 + 36t,0 ≤ t ≤ 3.For what value of t will n be a maximum?

A real estate firm owns 70 apartments.At $200 per month each apartment can be rented.However,for each $10 per month increase,there will be two vacancies with no possibility of filling them.What rent per apartment will maximize monthly revenue?

The demand function for a monopolist's product is p = 100 - 3q,where p is the price per unit (in dollars)for q units.If the average cost (in dollars)per unit for q units is = 4 + ,find the output q at which profit is maximized.

An open box is to have a surface area of 300 .The base of the box is to be a square.Find the dimensions of the box that maximize volume.

A cable TV company has 200 customers paying $10 each month.For each $1 reduction in price,the company attracts 50 more customers.Find the price that yields maximum revenue.

A manufacturer has determined that the total cost c of producing q units of a product is given by Average cost will be a minimum at a production level of

A company owns an apartment building containing 80 units.If the company charges $300 per month rent,then all units can be rented out,and for every increase of $10 per month in rent,the company will lose one customer.What rent should be charged to maximize revenue?