Exam 23: Linear Programming

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?

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

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 + $2Y what is the maximum profit the company can earn?

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

The Queen City Nursery manufactures bags of potting soil from compost and topsoil.Each cubic foot of compost costs 12 cents and contains 4 pounds of sand,3 pounds of clay,and 5 pounds of humus.Each cubic foot of topsoil costs 20 cents and contains 3 pounds of sand,6 pounds of clay,and 12 pounds of humus.Each bag of potting soil must contain at least 12 pounds of sand,at least 12 pounds of clay,and at least 10 pounds of humus.Formulate the problem as a linear program.Plot the constraints and identify the feasible region.Graphically or with corner points find the best combination of compost and topsoil that meets the stated conditions at the lowest cost per bag.Identify the lowest cost possible.

A synonym for shadow price is ________.

What is sensitivity analysis?

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