Question 1

Briefly describe the meaning of a shadow price.Provide an example of how a manager could use information about shadow prices to improve operations?

Accepted Answer

The answer of Briefly describe the meaning of a shadow...

Question 2

While glancing over the sensitivity report,you note that the stitching labor has a shadow price of $10 and a lower limit of 24 hours with an upper limit of 36 hours.If your original right hand value for stitching labor was 30 hours,you know that:
A)the next worker that offers to work an extra 8 hours should receive at least $80.
B)you can send someone home 6 hours early and still pay them the $60 they would have earned while on the clock.
C)you would be willing pay up to $60 for someone to work another 6 hours.
D)you would lose $80 if one of your workers missed an entire 8 hour shift.

Accepted Answer

The shadow price of $10 means that for every one additional hour of stitching labor, the company would be willing to pay up to $10. Therefore, if the company wanted an additional 6 hours of stitching labor (to reach the upper limit of 36 hours), they would be willing to pay up to $60 (6 x $10). This is the best choice because it is within the allowed range and will not result in over or underutilization of resources. Choice A is incorrect because it assumes the worker will work 8 extra hours, which is beyond the upper limit of availability. Choice B is incorrect because it involves underutilization of resources, and Choice D is incorrect because it assumes a worker would miss an entire 8-hour shift, which is not mentioned or allowed in the problem.

Question 3

________ is the amount by which the left-hand side falls short of the right-hand side in a linear programming model.

Accepted Answer

The answer of ________ is the amount by which the...

Question 4

Consider a corner point to a linear programming problem,which lies at the intersection of the following two constraints: 6X1 + 15X2 < 390 2X1 + X2 < 50 Which of the following statements about the corner point is TRUE? A)X1 < 21 B)X1 > 25 C)X1 < 10 D)X1 > 17

Accepted Answer

Solving the system of equations formed by the constraints gives the corner point. Substituting the values of X1 and X2 from the intersection point into the inequalities shows that X1 < 21.

Question 5

A(n)________ limits the ability to improve the objective function.

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The answer of A(n)________ limits the ability to improve the...

Question 6

In linear programming,a(n)________ is a point that lies at the intersection of two (or possibly more)constraint lines on the boundary of the feasible region.

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The answer of In linear programming,a(n)________ is a point that...

Question 7

The ________ is the upper and lower limit of an objective function coefficient over which the optimal values of the decision variables remain unchanged.

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The answer of The ________ is the upper and lower...

Question 8

For an "equal" constraint,only points ________ are feasible solutions.

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The answer of For an "equal" constraint,only points ________ are...

Question 9

For the line that has the equation 4X1 + 8X2 = 88,an axis intercept is:
A)(0,22).
B)(6,0).
C)(6,22).
D)(0,11).

Accepted Answer

The answer of For the line that has the equation...

Question 10

What does the feasible region represent?

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Question 11

A very confused manager is reading a two-page report given to him by his student intern."She told me that she had my problem solved,gave me this,and then said she was off to her production management course," he whined."I gave her my best estimates of my on-hand inventories and requirements to produce,but what if my numbers are slightly off? I recognize the names of our four models W,X,Y,and Z,but that's about it.Can you figure out what I'm supposed to do and why?" You take the report from his hands and note that it is the answer report and the sensitivity report from Excel's solver routine.
Explain each of the highlighted cells in layman's terms and tell the manager what they mean in relation to his problem.

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The answer of A very confused manager is reading a...

Question 12

The interval over which the right-hand-side parameter of a constraint can vary while its shadow price remains valid is the ________.

Accepted Answer

The answer of The interval over which the right-hand-side parameter...

Question 13

You observe a linear programming problem that has been solved using the graphical method of linear programming.The feasible region and optimal solution are clearly labeled.How could you identify the slack or surplus amounts in the scenario?

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The answer of You observe a linear programming problem that...

Question 14

A(n)________ is the marginal improvement in the objective function value caused by relaxing a constraint by one unit.

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The answer of A(n)________ is the marginal improvement in the...

Question 15

A modeler is limited to two or fewer decision variables when using the ________.

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The answer of A modeler is limited to two or...

Question 16

________ is the amount by which the left-hand side exceeds the right-hand side in a linear programming model.

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The answer of ________ is the amount by which the...

Question 17

Use the graphical technique to find the optimal solution for this objective function and associated constraints.
Maximize: Z = 8A + 5B
Subject To:
Constraint 1 4A + 5B < 80
Constraint 2 7A + 4B < 120
A,B > 0
a.Graph the problem fully in the following space.Label the axes carefully,plot the constraints,shade the feasibility region,identify all candidate corner points,and indicate which one yields the optimal answer.

Accepted Answer

The answer of Use the graphical technique to find the...

Question 18

What are the limitations of the graphical method of linear programming?

Accepted Answer

The answer of What are the limitations of the graphical...

Question 19

What is the meaning of a slack or surplus variable?

Accepted Answer

The answer of What is the meaning of a slack...

Question 20

A manager is interested in deciding production quantities for products A,B,and C.He has an inventory of 20 tons each of raw materials 1,2,3,and 4 that are used in the production of products A,B,and C.He can further assume that he can sell all of what he makes.Which of the following statements is CORRECT?
A)The manager has four decision variables.
B)The manager has three constraints.
C)The manager has three decision variables.
D)The manager can solve this problem graphically.

Accepted Answer

The manager has three decision variables (the production quantities for products A,B, and C), and since the inventory of each raw material is equal, there is only one constraint for each raw material used in the production of the three products. Therefore, the manager has three constraints. The problem can be solved graphically if the objective function and constraints are linear.

Quiz 19: Linear Programming