Question

The owner of a quick oil-change business charges $ 20 per oil change and has 40 customers per day. If each increase of $ 2 results in 2 fewer dailer customers, what price should the owner charge (to the nearest $ 2 ) for an oil change if the income from the business is to be as great as possible?

Answer 1

Answer:

maximum income is $900

Explanation:

given data

oil change = $20

per day = 40 customer

increase = $ 2

dailer customers = 2

owner charge = $ 2

to find out

income from the business

solution

we know current income is 40 × 20

current income = $800

we consider here price increase x and income as function y

so y = (20 +2x) × ( 40 - 2x)    ........1

y = −4x² + 40x + 800

take derivative and put dy/dx = 0 for maximum

dy/dx = -8x + 40

0 = -8x + 40

x=5

so here from 1

y = (20 +2x) × ( 40 - 2x)

y = (20 +2(5)) × ( 40 - 2(5))

y = 30 × 30

y = 900

so maximum income is $900