Answer: The answer is as follows:
Explanation:
Given that,
D(x) =140[tex]e^{-0.03x}[/tex]
Revenue Function, R(x) = x × D(x)
= 140x[tex]e^{-0.03x}[/tex]
For maximizing revenue,
R'(x) = 0
140[tex]e^{-0.03x}[/tex] + 140x[tex]e^{-0.03x}[/tex]×(-0.03) = 0
[tex]e^{-0.03x}[/tex](140-4.2x) = 0
x = [tex]\frac{140}{4.2}[/tex]
= [tex]\frac{100}{3}[/tex] ⇒ Number of units sold
Price = [tex]140e^{-0.03\times\frac{100}{3} }[/tex]
= 51.50 ⇒ price that will yield the maximum revenue
