Assignment: Linear Programming

1. Why is it important for an objective and its constraints to be linear?

2. What are the conditions causing linear programming problems to have multiple solutions?

3. Do you prefer the corner point method or the isoprofit, isocost method? Why?

4. Explain the purpose and procedures of the simplex method.

5. What is a shadow price? How does the concept relate to the dual of an LP problem? How does it relate to the primal?

6. Electrocomp's management realizes that it forgot to include two critical constraints. In particular, management decides that to ensure an adequate supply of air conditioners for a contract, at least 20 air conditioners should be manufactured. Because Electrocomp incurred an oversupply of fans in the preceding period, management also insists that no more than 80 fans be produced during this production period. Resolve this product mix problem to find the new optimal solution.

7. Management of Sundown Rent-a-Car has decided that perhaps the cost during the six-month period is not the appropriate Cost to minimize because the agency may still be obligated to additional months on some leases after that time. For example, if Sundown had some cars delivered at the beginning of the sixth month, Sundown would still he obligated for two additional months on a three-month lease. Use LP to determine how many cars should be leased in each month on each type of lease to minimize the cost of leasing over the entire life of these leases.