# Linear Programming, Assignment, Transportation Problems

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1. You are a manufacturer of tables and chairs. There are two types of wood and various amounts of labor required for each product. Specifically, each table requires 5 yards of walnut, 2 walnut, 3 yards of pine and 2 labor-hours. Each chair requires 2 yards of walnut, 2 yards of pine and 2 labor-hours. The manufacturer can sell all that is produce and make a profit of $12 per table and $8 per chair. For today, there are 150 yards of walnut, 100 yards of pine, and 80 labor-hours available. Set up the LP problem to include the 1st tableau.

2(a) Below is the 3d tableau of the above problem. Why is it optimal? How much of each product should be produced and at what profit?

(b) Just after you had finished your solution, it was discovered that an extra 5 labor-hours would be available, and there were only 95 yds of show work..

(c) It was also discovered that 8 extra yards of walnut were available. Discuss and show the implications of this.

(f) It has been found thru experience that chair costs could be implications of this change.

(g) Set up the dual and give its answers.

(h) Find the range of optimality

Determine the optimal assignment and compute total minimum time.

2. A plant has four workers to be assigned to four machines. The time (in minutes) require to produce a product by each worker on each machine is:

Determine the optimal assignment and compute total minimum time.

3. Solve the transportation problem having the costs, origin availabilities, and destination requirements below. Use VAM, MODI, and stepping stone methods to obtain the optimal solution.

Find the range of feasibility

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