Exam 18: Linear Programming

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.

The main disadvantage of introducing constraints into a linear program that enforce some or all of the decision variables to be either integer or binary is that:

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).

A craftsman builds two kinds of birdhouses, one for wrens (X1), and one for bluebirds (X2). Each wren birdhouse takes two hours of labor and two units of lumber. Each bluebird house requires three hours of labor and eight units of lumber. The craftsman has available 80 hours of labor and 160 units of lumber. Wren houses profit $4 each and bluebird houses profit $12 each. Use the software output that follows to interpret the problem solution. Include a statement of the solution quantities (how many of which product), a statement of the maximum profit achieved by your product mix, and a statement of "resources unused" and "shadow prices."

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

Very few linear programming problems involve minimizing an objective.

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

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

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.

A synonym for dual value is ________.

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?

A difference between minimization and maximization problems is that:

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

Describe how to incorporate fixed costs into a cost-minimizing linear program, where the fixed cost of using a machine is incurred if any products are produced on that machine.

Phil Bert's Nuthouse is preparing a new product, a blend of mixed nuts. The product must be at most 40% peanuts, must have more almonds than cashews, and must be at least 15% pecans. The blend will be sold in half-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 $5 per pound. Almonds cost $3 per pound, and pecans cost $6 per pound. Formulate this problem as a linear program.

What are the requirements of all linear programming problems?

Suppose that the feasible region of a maximization LP problem has corners of (0,0), (10,0), (5,5), and (0,7). If profit is given to be $X + $3Y what is the maximum profit the company can earn?

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

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?

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.