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:

Step-by-step 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 =
`(140)/(4.2)`

=
`(100)/(3)` ⇒ Number of units sold

Price =
`140e^{-0.03*(100)/(3) }`

= 51.50 ⇒ price that will yield the maximum revenue