Question

The demand for cat food is given by D ( x ) = 140 e − 0.03 x where x is the number of units sold and D(x) is the price in dollars. Find the revenue function. R ( x ) = Incorrect syntax error Find the number of units sold that will maximize the revenue. Find the price that will yield the maximum revenue.

Answer 1

Answer: The answer is as follows:

Explanation:

Given that,

D(x) =140$e^{-0.03x}$

Revenue Function, R(x) = x × D(x)

= 140x$e^{-0.03x}$

For maximizing revenue,

R'(x) = 0

140$e^{-0.03x}$ + 140x$e^{-0.03x}$×(-0.03) = 0

$e^{-0.03x}$(140-4.2x) = 0

x = $\frac{140}{4.2}$

= $\frac{100}{3}$ ⇒ Number of units sold

Price = $140e^{-0.03\times\frac{100}{3} }$

= 51.50 ⇒ price that will yield the maximum revenue