Boss Company currently leases a delivery van from Check Enterprises for a fee of $250 per month plus $0.40 per mile.Management is evaluating the desirability of switching to a modern,fuel-efficient van,which can be leased from David,Inc.,for a fee of $600 per month plus $0.05 per mile.All operating costs and fuel are included in the rental fees.Which delivery van would it be economically preferable to lease?
A)David,Inc.is economically preferable to a lease from Check Enterprises regardless of the monthly use.
B)Check Enterprises is economically preferable below 1,000 miles per month.
C)Check Enterprises is economically preferable to a lease from David,Inc.,regardless of the monthly use.
D)Check Enterprises is economically preferable above 1,000 miles per month.

Question

Quizplus · Accepted Answer

DTo determine the economically preferable option, we need to compare the total costs of leasing from both companies at various mileage levels. The cost functions for both companies are as follows:- Check Enterprises: $C_{Check} = 250 + 0.40m$, where $m$ is the number of miles driven per month.- David, Inc.: $C_{David} = 600 + 0.05m$.To find the break-even point where the costs are equal, we set $C_{Check} = C_{David}$:$$250 + 0.40m = 600 + 0.05m$$Solving for $m$ gives the mileage at which both options cost the same. Subtracting $0.05m$ from both sides and then subtracting 250 from both sides gives:$$0.35m = 350$$$$m = 1,000$$This means at 1,000 miles per month, both leasing options cost the same. Below 1,000 miles, Check Enterprises is cheaper because its fixed monthly fee is lower, and the higher per-mile cost has less impact due to fewer miles being driven. Above 1,000 miles, the lower per-mile cost of David, Inc. doesn't compensate for its higher fixed monthly fee, making Check Enterprises preferable due to its lower per-mile cost having a greater impact at higher mileages.

Boss Company Currently Leases a Delivery Van from Check Enterprises