a market sells cans of soda pop in machines. it finds that sales average 23,000 cans per month when the cans…

a market sells cans of soda pop in machines. it finds that sales average 23,000 cans per month when the cans sell for 50¢ each. for each nickel increase in the price, the sales per month drop by 1000 cans. (a) determine a function r(x) that models the total revenue realized by the market, where x is the number of $0.05 increases in the price of a can. (b) find a graph of r(x) that clearly shows a maximum for r(x). (c) how much should the market charge per can to realize the maximum revenue? what is the maximum revenue? (a) choose the correct function below. o a. r(x)=(23,000 - 1000x)(0.5 + 0.05x) o b. r(x)=(23,000 - 0.05x)(1000 - 0.5x) o c. r(x)=\frac{23,000 - 1000x}{0.5 - 0.05x} o d. r(x)=\frac{23,000 - 0.05x}{1000 - 0.5x}

a market sells cans of soda pop in machines. it finds that sales average 23,000 cans per month when the cans sell for 50¢ each. for each nickel increase in the price, the sales per month drop by 1000 cans. (a) determine a function r(x) that models the total revenue realized by the market, where x is the number of $0.05 increases in the price of a can. (b) find a graph of r(x) that clearly shows a maximum for r(x). (c) how much should the market charge per can to realize the maximum revenue? what is the maximum revenue? (a) choose the correct function below. o a. r(x)=(23,000 - 1000x)(0.5 + 0.05x) o b. r(x)=(23,000 - 0.05x)(1000 - 0.5x) o c. r(x)=\frac{23,000 - 1000x}{0.5 - 0.05x} o d. r(x)=\frac{23,000 - 0.05x}{1000 - 0.5x}

Answer

Explanation:

Step1: Recall revenue formula

Revenue = Price × Quantity. Initial price per can is $0.5$ and initial quantity is 23000. For each $x$ (number of $0.05$ - dollar increases in price), the price per can becomes $0.5 + 0.05x$ and the quantity sold becomes $23000-1000x$.

Step2: Form the revenue function

$R(x)=(23000 - 1000x)(0.5+0.05x)$

Answer:

A. $R(x)=(23000 - 1000x)(0.5+0.05x)$