Exam 2: Linear Programming: Model Formulation and Graphical Solution

The optimal solution for a graphical linear programming problem is the corner point that is the farthest from the origin.

Cully Turniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the storage space constraint?

The values of decision variables are continuous or divisible.

Consider the following linear programming problem: Max Z =    3x1 + 3x2 Subject to:    10x1 + 4x2 ? 60      25x1 + 50x2 ? 200     x1, x2 ? 0 Find the optimal profit and the values of x1 and x2 at the optimal solution.

The first step in formulating a linear programming model is to define the objective function

Proportionality means the slope of a constraint is proportional to the slope of the objective function.

An intern sets up a linear program to optimize the use of paper products in the men's washroom. The system of equations he develops is: Max 2T + 3S + 4ST S.t    3T + 6S ? 40    10T + 10S ? 66    10T + 15S ? 99 His mentor studies the model, frowns, and admonishes the intern for violating which of the following properties of linear programming models?

Slack variables are only associated with maximization problems.

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the objective function?

Cully Furniture buys two products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. If the furniture company purchases no big shelves and 200 medium shelves, which of the two resources will be completely used (at capacity)?

A constraint is a linear relationship representing a restriction on decision making.

Linear programming models exhibit linearity among all constraint relationships and the objective function.

Consider the following linear program: MIN Z = 60A + 50B s.t.  10A + 20B ? 200    8A + 5B ? 80    A ? 2    B ? 5 Solve this linear program graphically and determine the optimal quantities of A, B, and the value of Z.

Which of the following is not a typical characteristic of a linear programming problem?

The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeled Z*. -The equation for constraint DH is:

Consider the following minimization problem: Min z = x1 + 2x2    s.t. x1 + x2 ? 300    2x1 + x2 ? 400    2x1 + 5x2 ? 750    x1, x2 ? 0 Which constraints are binding at the optimal solution? (x1 =250, x2 = 50)

A minimization model of a linear program contains only surplus variables.

Decision variables

________ are mathematical symbols representing levels of activity.

Consider the following linear programming problem: MIN Z =    10x1 + 20x2 Subject to:    x1 + x2 ? 12     2x1 + 5x2 ? 40     x2 ? 13     x1, x2 ? 0 What is minimum cost and the value of x1 and x2 at the optimal solution?