Bountiful Boats has to produce at least 5000 cabin cruisers and 12,000 pontoons each year; they can produce at most 30,000 jet skis in a year. The company has two factories; one in Michigan, and one in Wisconsin; each factory is open for a maximum of 240 days per year. The Michigan factory makes 20 cabin cruisers, 40 pontoons, and 60 jet skis per day. The Wisconsin factory makes 10 cruisers, 30 pontoons, and 50 jet skis per day. The cost to run the Michigan factory per day is $960,000; the cost to run the Wisconsin factory per day is $750,000. How many days of the year should each factory run in order to meet the boat production, yet do so at a minimum cost? a) Formulate the linear programming problem.
b) Solve the system of equations using excel and solver. What is the optimal solution and cost?
c) Run a sensitivity report. Interpret/analyze the Constraint section of the sensitivity report clearly and concisely.
d) Base your answers on the sensitivity report and justify answers clearly. All changes apply to the original LP (changes are not cumulative).
1. Which constraint(s) are binding?
2. Bountiful Boats production people, feels that it must keep the Michigan factory open a maximum of 242 days per year, what effect will that have on its minimum cost? A new top executive wants to drop production at the Michigan factory by 10 days, what effect will that have on its minimum cost?
3. A local retailer has requested 500 additional pontoons, what effect will that have on its minimum cost?
4. A supplier of jet ski engine parts has cut back; therefore Bountiful Boasts can only produce at most 24,000 jet skis, what effect will that have on its minimum cost?