Question 1

Maximize
Z = 
- 2 
+ 3 
Subject to 
A) 0
B) 5
C) 10
D) 15
E) 20

Accepted Answer

The answer of Maximize
Z = 
- 2 
+ 3 
Subject...

Question 2

When no quotients exist in a simplex table,
A) a degenerate BFS will occur.
B) the problem has an unbounded solution.
C) there is a possibility for multiple optimum solutions.

Accepted Answer

When no quotients exist in a simplex table, it means that the pivot column has all non-positive entries. This implies that any pivot element will result in an increase in the objective function value. Since we cannot identify a direction to move towards an optimum solution, it indicates that the problem has an unbounded solution.

Question 3

Use the simplex method to minimize
Z = 3 
+ 2 
Subject to

, 
≥ 0
A) Z =  when  =  ,  = 0
B) Z = 21 when  = 7,  = 0
C) Z = 14 when  = 0,  = 7
D) Z = 14 when  = 7,  = 0

Accepted Answer

The answer of Use the simplex method to minimize
Z =...

Question 4

Maximize
Z = 10x + 15y
subject to

Accepted Answer

The answer of Maximize
Z = 10x + 15y
subject to ...

Question 5

A manufacturer produces two products,product A and product B.Both products require processing on Machines I and II.The number of hours needed to produce one unit is given by the following chart:  
Machine I is available for at most 1150 hours and Machine II is available for at most 1100 hours.If the profit made on product A is $15 / unit and the profit made on product B is $30 / unit.Find the production level that will maximize profit and find the Maximum profit.

Accepted Answer

The answer of A manufacturer produces two products,product A and...

Question 6

A person decides to take two different dietary supplements.Each supplement contains two essential ingredients,A and B,for which there are minimum daily requirements,and each contains a third ingredient,C,which needs to be minimized.Find the amount of each supplement that the person should take each day in order to satisfy the requirements for A and B while minimizing C.Also find the amount of C the person takes each day.

Accepted Answer

The answer of A person decides to take two different...

Question 7

Use the simplex method to
maximize
Z =  
+ 4  
+  
subject to  
.

Accepted Answer

The answer of Use the simplex method to
maximize
Z = ...

Question 8

A summer camp wants to hire counselors and aides to fill its staffing needs at minimum cost.The average monthly salary of a counselor is $2400 and the average monthly salary of an aide is $1100.The camp can accommodate up to 45 staff members and needs at least 30 to run properly.They must have at least 10 aides,and may have up to 3 aides for every 2 counselors.How many counselors and how many aides should the camp hire to minimize cost?
A) 12 counselors and 18 aides
B) 27 counselors and 18 aides
C) 35 counselors and 10 aides
D) 18 counselors and 12 aides

Accepted Answer

The camp should hire 12 counselors and 18 aides to minimize cost. This combination meets all of the camp's requirements and has the lowest total monthly salary cost.

Question 9

A company has two different locations to assemble three different models of PCs.The table below summarizes the daily production capacity,the minimum number of each type needed,and the daily operating costs for each location.Find the number of days that each location needs to operate in order to fill the orders at minimum cost.

Accepted Answer

The answer of A company has two different locations to...

Question 10

Give the dual of:
Maximize
Z =  
+ 3  
+ 4  
subject to
3  
+  
-  
≤ 4
4  
-  
+ 2  
≥ 1  
,  
,  
≥ 0.

Accepted Answer

The answer of Give the dual of:
Maximize
Z =  
+...

Question 11

In the initial simplex table below,find the pivot entry.

A) -1
B) 0
C) 10
D) 2
E) 6

Accepted Answer

The answer of In the initial simplex table below,find the...

Question 12

In the initial simplex table below,find the departing variable.

A) 
B) 
C) 
D) 
E) Z

Accepted Answer

The answer of In the initial simplex table below,find the...

Question 13

A company manufactures two models of inline skates,Alpha and Beta,at two different manufacturing plants.The maximum output at plant I is 1000 per month,while the maximum output at plant II is 1200 per month.Due to contractual obligations,the number of Alpha models produced at plant I must exceed the number of Beta models produced at plant I by at least 100.The profit per Alpha and Beta model manufactured at plant I is $50 and $80,respectively,while the profit per Alpha and Beta model manufactured at plant II is $60 and $70,respectively.This month,the company received an order for 900 Alpha and 1000 Beta models.Find how many of each model should be produced at each plant in order to satisfy the order and maximize the profit.(Hint: Let  
represent the number of Alpha models and  
represent the number of Beta models manufactured at plant I.)

Accepted Answer

The answer of A company manufactures two models of inline...

Question 14

A manufacturer produces two products,product A and product B.Both products require processing on Machines I and II.The number of hours needed to produce one unit is given by the following chart:  
Machine I is available for at most 1000 hours and Machine II is available for at most 2500 hours.If the profit made on product A is $20 / unit and the profit made on product B is $25 / unit.Find the production level that will maximize profit and find the Maximum profit.

Accepted Answer

The answer of A manufacturer produces two products,product A and...

Question 15

Use the simplex method to minimize
Z = 4  
+  
subject to  
+  
≥ 5  
+ 2  
≥ 8  
,  
≥ 0.

Accepted Answer

The answer of Use the simplex method to minimize
Z =...

Question 16

Maximize
Z = 4x + 6y
subject to

Accepted Answer

The answer of Maximize
Z = 4x + 6y
subject to ...

Question 17

Use the simplex method to
maximize
Z = 2  
- 3  
subject to  
+  
≥ 5  
+ 2  
≤ 8  
,  
≥ 0

Accepted Answer

The answer of Use the simplex method to
maximize
Z = 2...

Question 18

Use the simplex method to solve the following problem: United Blimpo Co.produces two types of exercise devices,regular and heavy-duty,each of which requires in its manufacture the use of two machines,A and B.A regular model requires the use of machine A for 2 hours and machine B for 3 hours.A heavy-duty model requires the use of machine A for 3 hours and machine B for 3 hours.Machine A can be used at most 18 hours a day and machine B can be used at most 21 hours a day.If the profits on the regular and heavy-duty models are $20 and $15,respectively,and United Blimpo Co.can sell all it produces,how many of each model should be produced per day in order to realize maximum profit? What is the maximum profit per day?

Accepted Answer

The answer of Use the simplex method to solve the...

Question 19

Use the simplex method to maximize
Z = 30x + 50y
subject to
2x + y ≤ 16
x + 2y ≤ 11
x + 3y ≤ 15
x,y ≥ 0

Accepted Answer

The answer of Use the simplex method to maximize
Z =...

Question 20

Use the simplex method to minimize
Z = -  
+ 2  
subject to  
+  
≤ 4
5  
+  
≥ -12
2  
+ 5  
≥ -14
3  
- 2  
≤ 17

Accepted Answer

The answer of Use the simplex method to minimize
Z =...

Quiz 8: Linear Programming

Maximize Z = - 2 + 3 Subject to

When no quotients exist in a simplex table,

Use the simplex method to minimize Z = 3 + 2 Subject to , ≥ 0

Maximize Z = 10x + 15y subject to

Use the simplex method to maximize Z = + 4 + subject to .

Give the dual of: Maximize Z = + 3 + 4 subject to 3 + - ≤ 4 4 - + 2 ≥ 1 , , ≥ 0.

In the initial simplex table below,find the pivot entry.

In the initial simplex table below,find the departing variable.

Use the simplex method to minimize Z = 4 + subject to + ≥ 5 + 2 ≥ 8 , ≥ 0.

Maximize Z = 4x + 6y subject to

Use the simplex method to maximize Z = 2 - 3 subject to + ≥ 5 + 2 ≤ 8 , ≥ 0

Use the simplex method to maximize Z = 30x + 50y subject to 2x + y ≤ 16 x + 2y ≤ 11 x + 3y ≤ 15 x,y ≥ 0

Use the simplex method to minimize Z = - + 2 subject to + ≤ 4 5 + ≥ -12 2 + 5 ≥ -14 3 - 2 ≤ 17