Define linear programming maximization and minimization models and use the graphs to solve these problems.

Use sensitivity analysis techniques to analyze business situations.

Formulate and solve the shipping, assignment and transshipment problems and use the solver to solve these applications.

Solve network models and problems including the shortest route, minimal spanning tree, and maximal flow applications.

Question one

In the following transportation model, use the northwest-corner method to find the starting solution.

Question two

Jo-Shop needs to assign four jobs it received to 4 workers. The varying skills of the workers give rise to varying costs for performing the jobs. Table 2 summarizes the cost data of the assignments. The data indicate that worker 1 cannot work on job 3, and worker 3 cannot work on job 4.

Question: Determine the optimal assignment.

Question three

Answer one of the following questions (question 1 or 2):

1- The Midwest TV Cable Company is in the process of providing cable service to ten new housing development areas. Figure 1 depicts the potential TV linkages among the five areas. The cable miles are shown on each branch.
Question: apply the Minimal Spanning tree to determine the most economical cable network.

2- Determine the shortest route between node 1 and node 8 in the network of Figure2.

Question four

Consider the following problem.

Max Z = 7x₁ + 4x₂

Subject to

6x₁ +4x₂ ≤ 24
x₁ + 2x₂ ≤ 6
x₁+ 2x₂ ≥ 4
x₂ ≤ 2
x₁, x₂ ≥ 0

1. Apply the graphical method to find the optimal solution to the linear programming problem above.

2. What is the effect of changing the constraint; x2 ≤ 2 to x2 ≤ 5 on the optimal solution found in the previous question?