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Complete questions C, D, and E. Need three pages of explanation.
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HACKNEY-RENT-A-CAR
The management at Hackney’s Southwestern Regional (HSR) are interested in determining the
optimal fleet purchase mix for the coming year. There are four types of vehicles that can be
purchased: standard, intermediate, compact and subcompact. All cars purchased are depreciated
and paid off for over a two-year period, after which they are sold in a secondary market. Table 1
presents the wholesale purchase price and revenues (the second year includes the resale value)
over the two-year period for each type of car:
Table 1 – Purchase Price and Net Revenue Summary
Type
Price ($)
1st yr. ($)
2nd yr. ($)
Standard
20,000
14,000
23,000
Intermediate
15,000
9,000
15,000
Compact
12,000
7,000
13,000
Subcompact
9,000
5,000
9,000
HSR has established a budget of $5 million for funding the purchases this year. It can either pay
the entire amount for the cars or make a down payment and pay the remaining balance over a
two-year period. The financing company requires a 20% down payment and that 50% of the
purchase price plus interest must be paid by the end of the first year. The financing company is
currently charging 8%. HSR uses a 10% discount rate for financial planning.
Hackney management estimates that they can rent all of the cars that are purchased. However, in
order to meet overall market demand they wish that each vehicle category represent at least 15
percent and no more than 50 percent of the total number of vehicles purchased.
a.
b.
c.
d.
e.
Formulate a linear programming model for this problem.
Define the basic assumptions associated with this problem.
Determine the optimal fleet-mix to purchase including the payment schedule.
What is the impact on the mix if the financing charge is reduced to 6%?
What is the impact on the mix if HSR requires at least 25% of each car type?
Be sure that your report includes a clear statement of what decision should be made and why. What
is the ideal purchase strategy?
1
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