When a wholesaler sells n CD players, the revenue is $R = 150 n - \frac { 1 } { 2 } n ^ { 2 }$ . How many CD players would the wholesaler have to sell to receive $\$ 11,250$ ?
A) $120$ CD players
B) $190$ CD players
C) $150$ CD players
D) $130$ CD players
E) $140$ CD players

Question

Quizplus · Accepted Answer

To find the number of CD players sold for a revenue of $11,250, we set the revenue equation equal to 11,250 and solve for $n$:$$11,250 = 150n - \frac{1}{2}n^2$$Rearranging the equation gives:$$\frac{1}{2}n^2 - 150n + 11,250 = 0$$Multiplying through by 2 to clear the fraction:$$n^2 - 300n + 22,500 = 0$$Factoring or using the quadratic formula, we look for factors of 22,500 that add up to 300. Recognizing that $150 \times 150 = 22,500$ and $150 + 150 = 300$, we can see that $n = 150$ is a solution.

When a Wholesaler Sells N CD Players, the Revenue Is R=150n−12n2R = 150 n - \frac { 1 } { 2 } n ^ { 2 }R=150n−21​n2

When a Wholesaler Sells N CD Players, the Revenue Is $R = 150 n - \frac { 1 } { 2 } n ^ { 2 }$