Ask Question
1 February, 04:52

The quantity demanded x for a product is inversely proportional to the cube of the price p for

p > 1.

When the price is $10 per unit, the quantity demanded is 125 units. The initial cost is $140 and the cost per unit is $2. What price will yield a maximum profit?

+5
Answers (1)
  1. 1 February, 07:46
    0
    X = k/p^3

    125 = k/10^3 = k/1000

    1000 x 125 = k

    k = 125000

    x = 125000/p^3

    The profit is given by G = px - (125 + 2x) = p (125000/p^3) - 125 - 2 (125000/p^3) = 125000/p^2 - 250000/p^3 - 125

    For maximum profit:

    dG/dp = 0

    dG/dp = - 250000/p^3 + 750000/p^4 = 0

    750000 - 250000p = 0

    p = 750000/250000 = 3

    Therefore the price that will yeaild maximum profit is $3.
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “The quantity demanded x for a product is inversely proportional to the cube of the price p for p > 1. When the price is $10 per unit, the ...” in 📘 Mathematics if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers