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Exam 22: Linear Programming

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Question 51

Multiple Choice

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If cars sell for $500 profit and trucks sell for $300 profit which of the following represents the objective function?

A) Maximize = 500C+300T
B) Minimize = 500C + 300T
C) Maximize = 500C - 300T
D) Minimize = 300T- 500C
E) None of the above

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Question 52

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

A) x = 2, y = 0
B) x = 0, y = 3
C) x = 0, y = 0
D) x = 1, y = 5
E) none of the above

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Question 53

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The optimal solution of a linear programming problem that consists of two variables and six constraints will probably not satisfy all six constraints as equalities.

A maximizing linear programming problem with constraints C1, C2, and C3 has been solved. The dual values associated with the problem are C1 = $2, C2 = $0.50, and C3 = $0. Which statement below is False?

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

What is sensitivity analysis?

A common form of the product-mix linear programming problem seeks to find that combination of products and the quantity of each that maximizes profit in the presence of limited resources.

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

An iso-profit line

The requirements of linear programming problems include an objective function, the presence of constraints, objective and constraints expressed in linear equalities or inequalities, and __________.

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

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

South Coast Papers wants to mix two lubricating oils (A and B) for its machines in order to minimize cost. It needs no less than 3,000 gallons in order to run its machines during the next month. It has a maximum oil storage capacity of 4,000 gallons. There are 2,000 gallons of Oil A and 4,000 of Oil B available. The mixed fuel must have a viscosity rating of no less than 40. When mixing fuels, the amount of oil obtained is exactly equal to the sum of the amounts put in. The viscosity rating is the weighted average of the individual viscosities, weighted in proportion to their volumes. The following is known: Oil A has a viscosity of 45 and costs 60 cents per gallon; Oil B has a viscosity of 37.5 and costs 40 cents per gallon. State the objective and the constraints of this problem. Plot all constraints and highlight the feasible region. Use your (by now, well-developed) intuition to suggest a feasible (but not necessarily optimal) solution. Be certain to show that your solution meets all constraints.

Using the iso-profit line solution method to solve a maximization problem requires that we

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. Write out the objective function and the constraints for this problem. (Hint: there are eight variables-chairs for building 1 cannot be used to satisfy the demands for another building).

In which of the following has LP been applied successfully?

Consider the following constraints from a two-variable linear program. (1) X ≥1 (2) Y ≥1 (3) X + Y ≤ 9 If these are the only constraints, which of the following points (X, Y) cannot be the optimal solution?

For a linear programming problem with the constraints 2X + 4Y ≤ 100 and 1X + 8Y ≤ 100, two of its corner points are (0, 0) and (0, 25).

Two methods of solving linear programming problems by hand include the corner-point method and the__________.

Suppose that an iso-profit line is given to be X+Y=15. What would be the profit made from producing 20X and 10Y?