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62. Break-Even Analysis A 2006 Chevrolet Impala costs $23,730 with a gasoline en

ID: 3030027 • Letter: 6

Question

62. Break-Even Analysis A 2006 Chevrolet Impala costs $23,730 with a gasoline engine. A 2006 Toyota Camry costs $25,900 with a hybrid engine. The Impala gets 20 miles per gallon of gasoline and the Camry gets 34 miles per gallon of gasoline. Assume that the price of gasoline is $2.909. (Source: Consumer Reports, March and August 2006) (a) Show that the cost Ce of driving the Chevrolet Impala x miles is Ce 23,730 2.909x/20 and the cost Ch of driving the Toyota Camry x miles is Ch 25,900 2.909x/34. (b) Find the break-even point. That is, find the mileage at which the hybrid-powered Toyota Camry becomes more economical than the gasoline-powered Chevrolet Impala.

Explanation / Answer

a) Lets assume x miles is driven

Impala : C(x) = fixed cost + varible cost

Varible cost = 2.909x/20

So,C(x) = 23730 + 2.909x/20

Camry : C(x) = fixed cost + varible cost

= 25900 + 2.909x/34

b) Ch(x) < Cg(x)

25900 + 2.909x/34 <  23730 + 2.909x/20

2170 < 0.05989x

x > 36233.09

x = 36233.09 miles

Ch = 25900 + 2.909*36233.09/34

= 29000.06 $

No. of gallons = 29000.06/2.909 = 9969.08

Avg per gallon = 36233.09/ 9969.08 = $3.63