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26 February, 12:00

Demand The demand function for the product is given by

p = 10,000 (1 - 3/3 + e^-0.001x)

where p is the price per unit (in dollars) and x is the number of units sold. Find the numbers of units sold for prices of (a) p = $500 and (b) p = $1500.

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  1. 26 February, 13:01
    0
    (a) 2996 units

    (b) 1897 units

    Step-by-step explanation:

    p = 10,000 (1 - 3/3 + e^-0.001x)

    (a) p = $500

    500 = 10,000 (1 - 1 + e^-0.001x)

    500/10,000 = e^-0.001x

    e^-0.001x = 0.05

    -0.001x = In 0.05 = - 2.996

    x = - 2.996/-0.001 = 2996 units

    (b) p = $1500

    1500 = 10,000 (1 - 3/3 + e^-0.001x)

    1500/10,000 = (1 - 1 + e^-0.001x)

    0.15 = e^-0.001x

    -0.001x = In 0.15 = - 1.897

    x = - 1.897/-0.001 = 1897 units
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