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Exam 23: Linear Programming Models

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Question 31

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Suppose that the feasible region of a maximization LP problem has corners of (0,0) , (5,0) ,and (0,5) .How many possible combinations of X and Y will yield the maximum profit if profit is given to be 5X + 5Y?

A) 0
B) 1
C) 2
D) 5
E) Infinite

F) A) and B)
G) B) and E)

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Question 32

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Phil Bert's Nuthouse is preparing a new product,a blend of mixed nuts.The product must be at most 50 percent peanuts,must have more almonds than cashews,and must be at least 10 percent pecans.The blend will be sold in one-pound bags.Phil's goal is to mix the nuts in such a manner that all conditions are satisfied and the cost per bag is minimized.Peanuts cost $1 per pound.Cashews cost $3 per pound.Almonds cost $5 per pound and pecans cost $6 per pound.Formulate this problem as a linear program.

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Call the variables PN,AL,CA,and PC
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Question 33

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Linear programming helps operations managers make decisions necessary to make effective use of resources such as machinery,labor,money,time,and raw materials.

A linear programming problem contains a restriction that reads "the quantity of X must be at least three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?

In linear programming,statements such as "the blend must consist of at least 10% of ingredient A,at least 30% of ingredient B,and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100 percent.

Which of the following is not a requirement of a linear programming problem?

________ is an analysis that projects how much a solution might change if there were changes in the variables or input data.

In linear programming,if there are three constraints,each representing a resource that can be used up,the optimal solution must use up all of each of the three resources.

In linear programming,a statement such as "maximize contribution" becomes an objective function when the problem is formulated.

The optimal solution to a linear programming problem lies within the feasible region.

The ________ is the set of all feasible combinations of the decision variables.

Two methods of conducting sensitivity analysis on solved linear programming problems are ________ and ________.

In a linear programming formulation,a statement such as "maximize contribution" becomes a(n) :

What combination of x and y will yield the optimum for this problem? Maximize $3x + $15y,subject to (1) 2x + 4y ≤ 12 and (2) 5x + 2y ≤ 10 and (3) x,y ≥ 0.

What is the region that satisfies all of the constraints in linear programming called?

The feasible region in the diagram below is consistent with which one of the following constraints?

Which of the following sets of constraints results in an unbounded maximization problem?

Suppose that the shadow price for assembly time is $5/hour.The allowable increase for the assembly time constraint is 40 hours,and the allowable decrease is 30 hours.If all assembly hours were used under the initial LP solution and workers normally make $4/hour but can work overtime for $6/hour,what should management do?

What combination of a and b will yield the optimum for this problem? Maximize $6a + $15b,subject to (1) 4a + 2b ≤ 12 and (2) 5a + 2b ≤ 20 and (3) x,y ≥ 0.

Which of the following is an algorithm for solving linear programming problems of all sizes?