Pre-Cal

posted by .

I've been trying to work this problem out for the past week and still havent managed to get to the answer.

jeans unlimited sold 6000 pairs of jeans in october at an average of 44$ each. The company president decides that she must increase the company's profits by increasing the price of a pair of jeans. Market research indicates that sales will drop 200 pairs for every 1$ increase in price. If the cost of making a pair of jeans is 25$ and all jeans made are sold , what price will maximize the profit?

The answer is 49.50$ but im not sure how to get there. I know that i somehow have to find a quadratic equation and find the derivative of that to find the max which will essentially give me enough information to find the final answer. PLEASE HELP.

  • Pre-Cal -

    Profit=NumberJeans*price-cost
    but numberjeans=6000-200(Price-44)

    profit=(6000-200(P-44))P-25
    I assume you know how to find max.
    dp/dPrice=0=(6000-200(P-44))+P(-200)(1)

    solve for P

    0=6000-200P+8800-200P
    400P=14,800
    P= 47 dollars. Check my work.
    I recommend on your graphing calculator graph the profit function
    Profit vs P

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Linda owns a jeans store. Her montly profit p( x) dollars on the sale of x pairs of jeans is given by the equation p(x ) = 50x - 1/5x^2. How many pairs of jeans must she sell each month to maximize her profit?
  2. math

    The fixed costs of oreparting a business are the costs include rent, fixed salaries, and costs of buying machinery. The variable costs of operating a business are the costs that change with the level of ouput. Variable costs include …
  3. math

    A pair of ordinary jeans at A-Mart costs $50 less than a pair of designer jeans at Enrico's. In fact, you can buy four pairs of A-Mart jeans for less than one pair of Enrico's jeans. What is the price range for a pair of A-Mart jeans?
  4. MaTH

    I am trying to work this problem and need help. Mary bought 2 pairs of identical jeans at a sale. She paid regular price for the first pair and paid half price for the second pair. If the total cost was $45.00,what was the regular …
  5. math

    pairs of jeans and want to take 2 with you. how many different ways can you pick 2 pairs of jeans.
  6. math (cant figure it out)

    you own 7 pairs of jeans and want to take 2 of them with you on vacation. In how many ways can you choose 2 pairs of jeans?
  7. math

    at a sale,josh bought 4 shirts and 3 pairs of jeans for $181.at the same store,mike bought 1 shirt and 2 pairs of jeans for $94.
  8. math

    You own 6 pairs of jeans and want to take 2 pairs on vacation with you. How many different ways can you take two pairs of jeans?
  9. writting skills

    Sentence 8:Be certain that you own one (and preferably,two) "business" outfits jeans, sandals,and tank tops ----------- will not impress any potential employer. Which of the following is the best way to write the underlined portion …
  10. math

    4. Thomas is at a store buying school clothes. T-shirts are on sale for $13 each and jeans are on sale for $18 each. a) Write an equation that represents the total cost for x T-shirts and y pairs of jeans. I need help with a.. b) Thomas …

More Similar Questions