Exam 19: Linear Programming

Suppose that 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?

John's Locomotive Works manufactures a model locomotive. It comes in two versions-a standard (X1), and a deluxe (X2). The standard version generates $250 per locomotive for the standard version, and $350 per locomotive for the deluxe version. One constraint on John's production is labour hours. He only has 40 hours per week for assembly. The standard version requires 250 minutes each, while the deluxe requires 350 minutes. John's milling machine is also a limitation. There are only 20 hours a week available for the milling machine. The standard unit requires 60 minutes, while the deluxe requires 120. Formulate as a linear programming problem, and solve using either the graphical or corner points solution method.

A linear programming maximization problem has been solved. In the optimal solution, two resources are scarce. If an added amount could be found for only one of these resources, how would the optimal solution be changed?

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?

The objective of a linear programming problem is to maximize 1.50A + 1.50B, subject to 3A + 2B ≤ 600, 2A + 4B ≤ 600, and 1A + 3B ≤ 420. a. Plot the constraints on the grid below b. Identify the feasible region and its corner points. Show your work. c. What is the optimal product mix for this problem?

What is linear programming?

A linear programming problem has three constraints: 2X + 10Y ≤ 1004X + 6Y ≤ 1206X + 3Y ≤ 90 What is the largest quantity of X that can be made without violating any of these constraints?

What is sensitivity analysis?

The difference between minimization and maximization problems is that

The region that satisfies all of the constraints in graphical linear programming is called the region of optimality.

A linear programming problem has two constraints 2X + 4Y = 100 and 1X + 8Y ≤ 100, plus non-negativity constraints on X and Y. Which of the following statements about its feasible region is true?

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. Item Cubic feet per Price per unit Weight per Can resell for Item Item 2\times4 studs 1 \ 0.10 5 pounds \ 0.80 4\times8 plywood 3 \ 0.50 20 pounds \ 3.00 Concrete blocks 0.5 \ 0.25 10 pounds \ 0.75 State the decision variables (give them labels). State the objective function. Formulate the constraints of this problem. Do not solve, but speculate on what might be a good solution for Tom. You must supply a set of quantities for the decision variables. Provide a sentence or two of support for your choice.

In which of the following has LP been applied successfully?

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

A company has the following usage of inputs, constraints on inputs and profit margins to make their three products. Product Wiring Drilling Assembly Profit X202 0.6 0.41 0.8 14 Y303 0.1 0.57 0.47 9.75 Z404 0.35 0.3 0.26 12.25 There are maximum amounts of the following: 1625 hours for wiring, 1750 hours for drilling and 1175 hours for Assembly. Make sure that the units produced are integers. Solve for the above problem. a) How many units of each product will be made? b) What is the maximum profit? c) Which input has the most amount of slack?

________ are restrictions that limit the degree to which a manager can pursue an objective.

Explain how to use the iso-profit line in a graphical maximization problem.

Suppose an LP problem was subject to constraints of 2X + Y> 10 X + 3Y> 20 Suppose that a new constraint is added, of the form 3X + A ∗ Y> 90. What is the largest value that A can have so that this new constraint is redundant?

In terms of linear programming, the fact that the solution is infeasible implies that the "profit" can increase without limit.