Exam 19: Linear Programming

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

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

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In a linear programming problem, what is the relationship between the constraints and the feasible region? Explain with reference to a problem with two variables.

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A stereo mail order centre has 8,000 cubic feet available for storage of its private label loudspeakers. The ZAR3 speakers cost $295 each and require 4 cubic feet of space; the ZAR2ax speakers cost $110 each and require 3 cubic feet of space; and the ZAR4 model costs $58 and requires 1 cubic foot of space. The demand for the ZAR3 is at most 20 units per month. The wholesaler has $100,000 to spend on loudspeakers this month. Each ZAR3 contributes $105, each ZAR2ax contributes $50, and each ZAR4 contributes $28. The objective is to maximize total contribution. Write out the objective and the constraints.

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Suppose that a constraint for assembly time has a shadow price of $50/hour for 15 hours in either direction and that all available assembly time is currently used (would require overtime to do more). If the salary of workers is $30 and they receive 50% extra pay for overtime what should management do?

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Which of the following combinations of constraints has no feasible region?

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The ________ is a mathematical expression in linear programming that maximizes or minimizes some quantity.

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Linear programming is an appropriate problem-solving technique for decisions that have no alternative courses of action.

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

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A linear programming problem contains a restriction that reads "the quantity of Q must be no larger than the sum of R, S, and T." Formulate this as a constraint ready for use in problem solving software.

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