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tatuchka [14]
3 years ago
13

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 dollar

s. 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.
Business
1 answer:
USPshnik [31]3 years ago
4 0

Answer: The answer is as follows:

Explanation:

Given that,

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

Revenue Function, R(x) = x × D(x)

= 140xe^{-0.03x}

For maximizing revenue,

R'(x) = 0

140e^{-0.03x} + 140xe^{-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

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