Question

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.

Answer 1

(a) 2996 units

(b) 1897 units

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