Mogul Motors is planning a major overhaul of its automobile assembly plants as it introduces 4 new models. Exactly one exisiting plant must be converted to assemble each model. The following table shows for each model and plant the cost (in millions of dollars) of modifications at the plant to produce the model. Those marked with a dash reflect plants not large enough to accommodate the needed activity.

Model Plant 1 2 3 4 1 18 26 — 31 2 — 50 22 —

3 40 29 52 39 4 — — 43 46 Mogul seek a minimum total cost way to make the conversion.

(a) Formulate this problem as a linear assignment LP.

(b) Explain why a binary optimal solution is guaranteed even though your model is a linear program.

(c) Use class optimization software to solve your assignment LP.