Question 1

A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $7,400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 3,300 labor-hours available. If he expects to make a profit of $100/acre on crop A and $140/acre on crop B, how many acres of each crop should he plant in order to maximize his profit?
​
__________ acres of crop A, __________ acres of crop B
​
What is the optimal profit? $ __________

Accepted Answer

The answer of A farmer plans to plant two crops,...

Question 2

A finance company has a total of $25 million earmarked for homeowner and auto loans. On the average, homeowner loans have a 8% annual rate of return, whereas auto loans yield a 12% annual rate of return. Management has also stipulated that the total amount of homeowner loans should be greater than or equal to 4 times the total amount of automobile loans. Determine the total amount of loans of each type the company should extend to each category in order to maximize its returns.
$ __________ million in homeowner loans, $ __________ million in auto loans
What are the optimal returns? (Round your answer to the nearest hundredth, if necessary).
$ __________ million

Accepted Answer

The answer of A finance company has a total of...

Question 3

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no.
Z = 5x + 8y  Max.: __________, min.: __________

Accepted Answer

The answer of Find the optimal (maximum and/or minimum) value(s)...

Question 4

Solve the linear programming problem by the method of corners.
  x = __________; y = __________; C = __________

Accepted Answer

The answer of Solve the linear programming problem by the...

Question 5

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no.
Z = x + 9y  Max.: __________, min.: __________

Accepted Answer

The answer of Find the optimal (maximum and/or minimum) value(s)...

Question 6

Find the optimal (maximum and minimum) values of the objective function on the feasible set S. If no maximum or minimum value exists, enter no.
​  ​  ​  __________,  __________

Accepted Answer

The answer of Find the optimal (maximum and minimum) values...

Question 7

Solve the linear programming problem by the method of corners.  x = __________; y = __________; P = __________

Accepted Answer

The answer of Solve the linear programming problem by the...

Question 8

A hunger-relief organization, has earmarked between $2 and $2.5 million, inclusive, for aid to two African countries, country A and country B. Country A is to receive between $1 and $1.5 million, inclusive, in aid, and country B is to receive at least $0.75 million in aid. It has been estimated that each dollar spent in country A will yield an effective return of $.60, whereas a dollar spent in country B will yield an effective return of $.50. How should the aid be allocated if the money is to be utilized most effectively according to these criteria? (Hint: If x and y denote the amount of money to be given to country A and country B, respectively, then the objective function to be maximized is P = 0.6x + 0.5y.)
$ __________ million to country A and $ __________ million to country B

Accepted Answer

The answer of A hunger-relief organization, has earmarked between $2...

Question 9

Solve the linear programming problem by the method of corners.  
 x = __________; y = __________; P = __________

Accepted Answer

The answer of Solve the linear programming problem by the...

Question 10

Solve the linear programming problem by the method of corners.  x = __________; y = __________; C = __________

Accepted Answer

The answer of Solve the linear programming problem by the...

Question 11

Solve the following linear programming problem by the method of corners.   __________  __________  __________

Accepted Answer

The answer of Solve the following linear programming problem by...

Question 12

Solve the linear programming problem by the method of corners.
Find the maximum and minimum of  subject to      Max: x = __________; y = __________; P = __________
Min: x = __________; y = __________; P = __________

Accepted Answer

The answer of Solve the linear programming problem by the...

Question 13

Solve the linear programming problem by the method of corners.  x = __________; y = __________; P = __________

Accepted Answer

The answer of Solve the linear programming problem by the...

Question 14

Find the optimal (maximum and minimum) values of the objective function on the feasible set  . If no maximum or minimum value exists, enter no.    __________,  __________

Accepted Answer

The answer of Find the optimal (maximum and minimum) values...

Question 15

A corporation has a division that produces two models of fireplace grates, model A and model B. To produce each model A grate requires 3 lb of cast iron and 6 min of labor. To produce each model B grate requires 4 lb of cast iron and 3 min of labor. The profit for each model A grate is $3.00, and the profit for each model B grate is $2.50. If 1,000 lb of cast iron and 20 labor-hours are available for the production of fireplace grates per day, how many grates of each model should the division produce in order to help maximize the division's profits?
__________ model A, __________ model B
What is the optimal profit?
$__________

Accepted Answer

The answer of A corporation has a division that produces...

Question 16

Solve the linear programming problem by the method of corners.
Maximize  subject to      x = __________; y = __________; P = __________

Accepted Answer

The answer of Solve the linear programming problem by the...

Question 17

Solve the linear programming problem by the method of corners.  
 x = __________; y = __________; P = __________

Accepted Answer

The answer of Solve the linear programming problem by the...

Question 18

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no.
Z = 8x + 6y  Max.: __________, min.: __________

Accepted Answer

The answer of Find the optimal (maximum and/or minimum) value(s)...

Question 19

Solve the linear programming problem by the method of corners.
  x = __________; y = __________; C = __________

Accepted Answer

The answer of Solve the linear programming problem by the...

Question 20

Perth Mining Company operates two mines for the purpose of extracting gold and silver. The Saddle Mine costs $14,000/day to operate, and it yields 50 oz of gold and 3,000 oz of silver each day. The Horseshoe Mine costs $16,000/day to operate, and it yields 75 oz of gold and 1,000 oz of silver each day. Company management has set a target of at least 650 oz of gold and 18,000 oz of silver. How many days should each mine be operated so that the target can be met at a minimum cost?
Saddle Mine: __________ days; Horseshoe Mine: __________ days
What is the minimum cost? $ __________

Accepted Answer

The answer of Perth Mining Company operates two mines for...

Quiz 3: Linear Programming: a Geometric Approach

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no. Z = 5x + 8y Max.: , min.:

Solve the linear programming problem by the method of corners. x = ; y = ; C = __

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no. Z = x + 9y Max.: , min.:

Find the optimal (maximum and minimum) values of the objective function on the feasible set S. If no maximum or minimum value exists, enter no. ,

Solve the linear programming problem by the method of corners. x = ; y = ; P = __

Solve the linear programming problem by the method of corners. x = ; y = ; P = __

Solve the linear programming problem by the method of corners. x = ; y = ; C = __

Solve the following linear programming problem by the method of corners. __

Solve the linear programming problem by the method of corners. Find the maximum and minimum of subject to Max: x = ; y = ; P = Min: x = ; y = ; P =

Solve the linear programming problem by the method of corners. x = ; y = ; P = __

Find the optimal (maximum and minimum) values of the objective function on the feasible set . If no maximum or minimum value exists, enter no. ,

Solve the linear programming problem by the method of corners. Maximize subject to x = ; y = ; P = __

Solve the linear programming problem by the method of corners. x = ; y = ; P = __

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no. Z = 8x + 6y Max.: , min.:

Solve the linear programming problem by the method of corners. x = ; y = ; C = __

Quiz 3: Linear Programming: a Geometric Approach

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no. Z = 5x + 8y Max.: __________, min.: __________

Solve the linear programming problem by the method of corners. x = __________; y = __________; C = __________

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no. Z = x + 9y Max.: __________, min.: __________

Find the optimal (maximum and minimum) values of the objective function on the feasible set S. If no maximum or minimum value exists, enter no. ​ ​ ​ __________, __________

Solve the linear programming problem by the method of corners. x = __________; y = __________; P = __________

Solve the linear programming problem by the method of corners. x = __________; y = __________; P = __________

Solve the linear programming problem by the method of corners. x = __________; y = __________; C = __________

Solve the following linear programming problem by the method of corners. __________ __________ __________

Solve the linear programming problem by the method of corners. Find the maximum and minimum of subject to Max: x = __________; y = __________; P = __________ Min: x = __________; y = __________; P = __________

Solve the linear programming problem by the method of corners. x = __________; y = __________; P = __________

Find the optimal (maximum and minimum) values of the objective function on the feasible set . If no maximum or minimum value exists, enter no. __________, __________

Solve the linear programming problem by the method of corners. Maximize subject to x = __________; y = __________; P = __________

Solve the linear programming problem by the method of corners. x = __________; y = __________; P = __________

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no. Z = 8x + 6y Max.: __________, min.: __________

Solve the linear programming problem by the method of corners. x = __________; y = __________; C = __________

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no. Z = 5x + 8y Max.: , min.:

Solve the linear programming problem by the method of corners. x = ; y = ; C = __

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no. Z = x + 9y Max.: , min.:

Find the optimal (maximum and minimum) values of the objective function on the feasible set S. If no maximum or minimum value exists, enter no. ,

Solve the linear programming problem by the method of corners. x = ; y = ; P = __

Solve the linear programming problem by the method of corners. x = ; y = ; P = __

Solve the linear programming problem by the method of corners. x = ; y = ; C = __

Solve the following linear programming problem by the method of corners. __

Solve the linear programming problem by the method of corners. Find the maximum and minimum of subject to Max: x = ; y = ; P = Min: x = ; y = ; P =

Solve the linear programming problem by the method of corners. x = ; y = ; P = __

Find the optimal (maximum and minimum) values of the objective function on the feasible set . If no maximum or minimum value exists, enter no. ,

Solve the linear programming problem by the method of corners. Maximize subject to x = ; y = ; P = __

Solve the linear programming problem by the method of corners. x = ; y = ; P = __

Find the optimal (maximum and/or minimum) value(s) of the given objective function on the feasible set S. If no maximum or minimum value exists, enter no. Z = 8x + 6y Max.: , min.:

Solve the linear programming problem by the method of corners. x = ; y = ; C = __