school
Acemy

Optimization

AP Calculus AB· difficulty 3/5

A shop sells 100100 items at \

<div class="math-block" data-math="10%24%20each.%20For%20each%20%5C"></div> 1$ price increase, sales drop by $5$ items. Maximum revenue?
  • A

    $$1000$

  • B

    $$1250$

  • C

    $$1500$

  • D

    $$1125$

    check_circle

Explanation

Price p=10+xp = 10 + x, quantity q=100−5xq = 100 - 5x. Revenue R=(10+x)(100−5x)=1000+50x−5x2R = (10+x)(100 - 5x) = 1000 + 50x - 5x^2. R′=50−10x=0⇒x=5,p=15R' = 50 - 10x = 0 \Rightarrow x = 5, p = 15, q=75q = 75, R=1125R = 1125.

Want 10 more like this — adaptive to your weak spots?

Practice 10 like thisarrow_forwardPredict my AP score

Related questions

auto_awesomeAll Toolsquestion_answerHomework Q&Amenu_bookAP & SAT PreptimelineLearn Mode