Ask Question
5 September, 20:12

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?

+2
Answers (1)
  1. 5 September, 22:57
    0
    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
Know the Answer?
Not Sure About the Answer?
Get an answer to your 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 ...” in 📙 Business if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions.
Search for Other Answers