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?

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