Ask Question
28 August, 07:49

The Acme Widget Company has found that if widgets are priced at s 389, then 1000 will be sold. They have also found that for every increase of $ 10, there will be 600 fewer widgets sold. The marginal cost of widgets is $ 97.25. The fixed costs for the Acme Widget Company are $ 8000. lf x represents the price of a widget find the following in terms of x The number of widgets that will be sold: The revenue generated by the sale of widgets: The cost of producing just enough widgets to meet demand: The proft from selling widgets: Find the price that will maximize profits from the sale of widgets:

+5
Answers (1)
  1. 28 August, 07:55
    0
    See the explanation below.

    Explanation:

    a. The number of widgets that will be sold

    Let y represent the number of widgets that will be sold, and and we already have x as price of widget, we therefore have:

    y - 1,000 = (-600/10) * (x - 389)

    y - 1,000 = - 60 * (x - 389)

    y = 1,000 - [60 * (x - 389) ]

    y = 1,000 - 60x + 23,340

    y = 24,340 - 60x

    b. The revenue generated by the sale of widgets

    Let R represent Revenue, therefore we have:

    R = xy

    R = x (24,340 - 60x)

    R = 24,340x - 60x²

    c. The cost of producing just enough widgets to meet demand

    Let C represent total cost, we therefore have:

    C = 8,000 + 97.25y

    C = 8,000 + 97.25 (24,340 - 60x)

    C = 8,000 + 2,367,065 - 5,835x

    C = 2,375,065 - 5,835x

    d. The proft from selling widgets

    Let P represent profit, we therefore have:

    P = R - C

    P = 24,340x - 60x² - (2,375,065 - 5,835x)

    P = 24,340x - 60x² - 2,375,065 + 5,835x

    P = - 60x² + 30,175x - 2,375,065

    e. Find the price that will maximize profits from the sale of widgets

    Profit is optimum when dP/dx = 0

    Therefore, we have

    0 = - 120x + 30,175

    120x = 30,175

    x = 30,175/120 = $251.46
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The Acme Widget Company has found that if widgets are priced at s 389, then 1000 will be sold. They have also found that for every increase ...” in 📗 Business if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers