The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by
$q = - 0.5 x + 170$ where q is the number of buggies it can sell in a month if the price is $x per buggy. What is the largest monthly revenue Round your answer to the nearest dollar.
A)$85
B) $14,450
C) $170
D) $7,225
E) $28,900

Question

The market research department of the Better Baby Buggy Co. predicts that the demand equation for its buggies is given by 
$q = - 0.5 x + 170$ where q is the number of buggies it can sell in a month if the price is $x per buggy. What is the largest monthly revenue  Round your answer to the nearest dollar.  
A)$85
B) $14,450
C) $170
D) $7,225
E) $28,900

Quizplus · Accepted Answer

To find the largest monthly revenue, we need to find the revenue function and then maximize it. Revenue (R) is calculated as price per unit (x) times quantity sold (q), so $R = xq$. Substituting the given demand equation $q = -0.5x + 170$ into the revenue function, we get $R = x(-0.5x + 170)$ or $R = -0.5x^2 + 170x$. To maximize revenue, we take the derivative of R with respect to x and set it to zero. The derivative of $R = -0.5x^2 + 170x$ is $R' = -x + 170$. Setting $R' = 0$ gives $x = 170$. Substituting $x = 170$ back into the revenue function, we get $R = -0.5(170)^2 + 170(170) = -0.5(28900) + 28900 = 14450$. Therefore, the largest monthly revenue is $14,450.

The Market Research Department of the Better Baby Buggy Co q=−0.5x+170q = - 0.5 x + 170q=−0.5x+170

The Market Research Department of the Better Baby Buggy Co $q = - 0.5 x + 170$