Exam 23: Linear Programming

Phil Bert's Nuthouse is preparing a new product,a blend of mixed nuts.The product must be at most 50 percent peanuts,must have more almonds than cashews,and must be at least 10 percent pecans.The blend will be sold in one-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 $3 per pound.Almonds cost $5 per pound and pecans cost $6 per pound.Formulate this problem as a linear program.

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

A difference between minimization and maximization problems is that:

The ________ is the set of all feasible combinations of the decision variables.

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

What are the requirements of all linear programming problems?

Two methods of conducting sensitivity analysis on solved linear programming problems are ________ and ________.

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

What is sensitivity analysis?

A craftsman builds two kinds of birdhouses,one for wrens (X1),and one for bluebirds (X2).Each wren birdhouse takes four hours of labor and four units of lumber.Each bluebird house requires two hours of labor and twelve units of lumber.The craftsman has available 60 hours of labor and 120 units of lumber.Wren houses profit $6 each and bluebird houses profit $15 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."

A linear programming problem contains a restriction that reads "the quantity of S must be no more than one-fourth as large as T and U combined." Formulate this as a linear programming constraint.

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.

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

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

In linear programming,if there are three constraints,each representing a resource that can be used up,the optimal solution must use up all of each of the three resources.

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

A firm makes two products,Y and Z.Each unit of Y costs $10 and sells for $40.Each unit of Z costs $5 and sells for $25.If the firm's goal were to maximize profit,what would be the appropriate objective function?

Binary variables can only take on the values of 1 or 2.

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?

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