The Cool Company determines that the supply function for its basic air conditioning unit is $S ( p ) = 50 + 0.01 p ^ { 3 }$ and that its demand function is $D ( p ) = 250 - 0.2 p ^ { 2 }$, where $p$ is the price. Determine the price for which the supply equals the demand.
A) $22.86
B) $21.86
C) $21.36
D) $22.36

Question

Quizplus · Accepted Answer

To find the price where supply equals demand, set $S(p) = D(p)$: $50 + 0.01p^3 = 250 - 0.2p^2$. Solving this equation for $p$ gives $p \approx 21.86$.

The Cool Company Determines That the Supply Function for Its S(p)=50+0.01p3S ( p ) = 50 + 0.01 p ^ { 3 }S(p)=50+0.01p3

The Cool Company Determines That the Supply Function for Its $S ( p ) = 50 + 0.01 p ^ { 3 }$