Exam 23: Linear Programming

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.

In which of the following has LP been applied successfully?

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?

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

In linear programming,a statement such as "maximize contribution" becomes an objective function when the problem is formulated.

The objective of a linear programming problem is to maximize 1.50A + 1.50B,subject to 3A + 2B ≤ 600,2A + 4B ≤ 600,1A + 3B ≤ 420,and A,B ≥ 0. a.Plot the constraints on the grid below c.Identify the feasible region and its corner points.Show your work. d.What is the optimal product mix for this problem?

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

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."

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?

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

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

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.

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

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

The corner-point solution method requires:

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.

In linear programming,statements such as "the blend must consist of at least 10% of ingredient A,at least 30% of ingredient B,and no more than 50% of ingredient C" can be made into valid constraints even though the percentages do not add up to 100 percent.

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

For the constraints given below,which point is in the feasible region of this maximization problem? (1)14x + 6y ≤ 42 (2)x - y ≤ 3 (3)x,y ≥ 0

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.