Exam 23: Linear Programming

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.

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

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

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

In sensitivity analysis,a zero shadow price (or dual value)for a resource ordinarily means that the resource has not been used up.

A shadow price (or dual value)reflects which of the following in a maximization problem?

Solving a linear programming problem with the iso-profit line solution method requires that we move the iso-profit line to each corner of the feasible region until the optimum is identified.

What combination of a and b will yield the optimum for this problem? Maximize $6a + $15b,subject to (1)4a + 2b ≤ 12 and (2)5a + 2b ≤ 20 and (3)x,y ≥ 0.

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

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).

For the following constraints,which point is in the feasible region of this minimization problem? (1)14x + 6y ≥ 42 (2)x - y ≥ 3

Data Corp.is considering which of 4 different projects to undertake in order to maximize its net present value (NPV).Define Xi as a binary variable that equals 1 if project i is undertaken and 0 otherwise,for i = 1,2,3,4.The NPV and required capital (in millions)for each project are listed below. Which of the following represents the constraint stating that project 3 can be undertaken only if project 2 is undertaken?

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 ≤ 600,1A + 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?

Sensitivity analysis can be applied to linear programming solutions by either (1)trial and error or (2)the analytic postoptimality method.

A maximizing linear programming problem has two constraints: 2X + 4Y ≤ 100 and 3X + 10Y ≤ 210,in addition to constraints stating that both X and Y must be nonnegative.What are the corner points of the feasible region of this problem?

A linear programming problem contains a restriction that reads "the quantity of X must be at least three times as large as the quantity of Y." Which of the following inequalities is the proper formulation of this constraint?

In the graphical solution to a linear program,the region that satisfies the constraint 4X + 15Z ≥ 1000 includes the origin of the graph.

Linear programming helps operations managers make decisions necessary to make effective use of resources such as machinery,labor,money,time,and raw materials.