If the price for a product is given by $p = 6400 - x ^ { 2 }$, where $x$ is the number of units sold, then the revenue is given by $R = p x = 6400 x - x ^ { 3 }$. How many units must be sold to give zero revenue?
A) 6400
B) 0, 6400
C) 0, 80
D) 0

Question

Quizplus · Accepted Answer

To find the number of units that must be sold to give zero revenue, we set the revenue equation $R = 6400x - x^3$ equal to zero and solve for $x$. This gives us the equation $0 = 6400x - x^3$, which simplifies to $x^3 = 6400x$. Factoring out $x$, we get $x(x^2 - 6400) = 0$, which gives us the solutions $x = 0$ and $x^2 = 6400$. Solving $x^2 = 6400$ gives $x = \pm 80$, but since the number of units sold cannot be negative, the valid solutions are $x = 0$ and $x = 80$.

If the Price for a Product Is Given By p=6400−x2p = 6400 - x ^ { 2 }p=6400−x2

If the Price for a Product Is Given By $p = 6400 - x ^ { 2 }$