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Calculus/Rate of Change
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Question
A paint store sells 270 cans of paint per month at a price of $32 each. A customer survey indicates that for each $1.20 decrease in price, sales will increase by six cans of paint.
a) Determine the demand, or price, function.
b) Determine the revenue function.
c) Determine the marginal revenue function.
d) Solve R'(x)=0. Interpret this value for this situation.
e) What price corresponds to the value found in part d)?
Thanks!
a) N = 270 + 6(x/1.2), where N is the number sold and x is the decrease in price.
b) The revenue function would be the product of the price and the number sold.
The price is 32 - 1.2x and the number is 270+6x, so it is P(x) = (32 - 1.2x)(270 + 6x).
c) To find the marginal revenue, compute the function as defined above, multiply it out,
and then take ther derivative.
d) When R'(x) = 0, the sales on additional cans by further reduction in price will drive the revenue down whereas the reduction in price so far has increased the revenue.
e) The price at that x value found in (d) where price was 32 - 1.2x.
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