Exam 23: Linear Programming Models

A stereo mail order center 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.Formulate this problem as a linear program.

A linear programming problem contains a restriction that reads "the quantity of X must be at least twice as large as the quantity of Y." Formulate this as a linear programming constraint.

What are corner points? What is their relevance to solving linear programming problems?

Which of the following correctly describes all iso-profit lines for an LP maximization problem?

What is the usefulness of a shadow price (or dual value)?

Suppose that an iso-profit line is given to be X + Y = 10.Which of the following represents another iso-profit line for the same scenario?

A linear programming problem has three constraints,plus nonnegativity constraints on X and Y.The constraints are: 2X + 10Y ≤ 100;4X + 6Y ≤ 120;6X + 3Y ≥ 90. What is the largest quantity of X that can be made without violating any of these constraints?

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

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 linear programming constraint.

The graphical method of solving linear programs can handle only maximization problems.

A difference between minimization and maximization problems is that:

Tom is a habitual shopper at garage sales.Last Saturday he stopped at one where there were several types of used building materials for sale.At the low prices being asked,Tom knew that he could resell the items in another town for a substantial gain.Four things stood in his way: he could only make one round trip to resell the goods;his pickup truck bed would hold only 1000 pounds;the pickup truck bed could hold at most 70 cubic feet of merchandise;and he had only $200 cash with him.He wants to load his truck with the mix of materials that will yield the greatest profit when he resells them. Formulate this problem as a linear program.

Which of the following represents a valid constraint in linear programming?

The corner-point solution method requires:

One requirement of a linear programming problem is that the objective function must be expressed as a linear equation.

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

The property manager of a city government issues chairs,desks,and other office furniture to city buildings from a centralized distribution center.Like most government agencies,it operates to minimize its costs of operations.In this distribution center,there are two types of standard office chairs,Model A and Model B.Model A is considerably heavier than Model B,and costs $20 per chair to transport to any city building;each model B costs $14 to transport.The distribution center has on hand 400 chairs-200 each of A and B. The requirements for shipments to each of the city's buildings are as follows: Building 1 needs at least 100 of A Building 2 needs at least 150 of B. Building 3 needs at least 100 chairs,but they can be of either type,mixed. Building 4 needs 40 chairs,but at least as many B as A. Formulate this problem as a linear program.(Hint: there are eight decision variables because we need to know how many of each chair (A and B)to deliver to each of the four buildings).

Suppose that a constraint is given by X + Y ≤ 10.If another constraint is given to be 3X + 2Y ≥ 15,and if X and Y are restricted to be nonnegative,determine the corners of the feasible solution.If the profit from X is 5 and the profit from Y is 10,determine the combination of X and Y that will yield maximum profit.

A synonym for shadow price is ________.

________ is a mathematical technique designed to help operations managers plan and make decisions necessary to allocate resources.