Question

if the income and cost curves are determined by the following equations:

income= 64SL^3

cost= 128SL^4

determine the service level that maximizes profit.

a) service level 100%

b) service level 25%

c) service level 50%

d) service level 75%

Answer 1

(a) If Service Level is 100%

Income = 64SL^3 = 64*1^3 = 64

Cost = 128Sl^4 = 128*1^4 =128

Profit = Income - Cost = -64

(b) If Service level is 25%

Income = 64SL^3 = 64*(0.25)^3 = 64*0.015625 = 1

Cost = 128Sl^4 = 128*(0.25)^4 =128*0.00390625 = 0.5

Profit = Income - Cost = 0.5

(c) If Service level is 50%

Income = 64SL^3 = 64*(0.5)^3 = 64*0.125 = 8

Cost = 128Sl^4 = 128*(0.5)^4 =128*0.0625 = 8

Profit = Income - Cost = 0

(d) If Service level is 75%

Income = 64SL^3 = 64*(0.75)^3 = 64*0.421875 = 27

Cost = 128Sl^4 = 128*(0.75)^4 =128*0.31640625 = 40.5

Profit = Income - Cost = -13.5

As per above calculations, Service Level which maximises profit is 25%. Answer is (b)