x bicycles will be sold.

a) Find an expression for the total revenue from the sale of x bicycles. (Hint: revenue = demand x price)

b) Find the number of bicycle sales that leads to maximum revenue.

c) Find the maximum revenue.

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One Response to The manager of a bicycle shop has found that, at a price (in dollars) of p(x) = 150 – x/4 per bicycle,?

  1. wayne.alexander@ymail.com says:

    [^2 denotes to the power of 2, or squared in other words]

    Price = 150 - x/4
    Demand = x

    Revenue = demand x price
    Revenue = x(150 - x/4)
    Revenue = 150x - x^2/4

    Stationary points (maximum/minimum points) occur when R' = 0

    R = 150x - x^2/4
    R' = 150 - 2x/4
    R' = 150 - x/2

    when R' = 0

    0 = 150 - x/2
    x/2 = 150
    x = 300 (stationary point - assume maximum as only one point exists)

    Use revenue equation to find revenue at maximum point:

    R = 150(300) - 300^2/4
    R = 45000 - 22500
    R = $22,500

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