J. Hazelwood Inc. operates a number of boat rentals at various resorts throughout the United States. Hazelwood is currently in the process of opening a boat rental on the Salton Sea. They plan to rent pontoons, runabouts, and wave runner. Hazelwood needs to determine the number of each type of rental to purchase. The purchasing costs are $60,000 for each pontoon, $20,000 for each runabout, and $10,000 for each wave runner. Hazelwood has set the maximum purchasing budget to $480,000. The annual upkeep and storage costs per product are estimated to be $800, $1,100, and $700 for pontoons, runabouts, and wave runners, respectively. The annual budget for upkeep and storage cost is $20,000. The annual cost for various insurance and liability coverage is $1,500 for each pontoon boat, $1,800 for each runabout, and $2,400 for each wave runner. Hazelwood wants to keep the insurance cost to no more than $42,000 a year. Hazelwood has decided they need to have at least three pontoon boats for regular customers who occasionally wish to host parties. In addition the market demand suggests Hazelwood needs to purchase at least one wave runner for every two runabouts purchased. The expected weekly revenue is $1500 for each pontoon, while the weekly revenue for runabouts is $1,700 and $800 for each wave runner. Formulate the LP model to maximize weekly revenue.
a. What is the maximum weekly revenue? _____________
b. What is the annual amount that will be spent on insurance and liability coverage?_______
c. What would be the maximum weekly revenue if the purchasing budget was equal to $50,000?
d. At what cut off value for weekly revenue would less runabouts be purchased? ________
e. What would be the maximum weekly revenue if only two pontoon boats needed to be purchased?