Solve the problem.
-Photon Lighting Company determines that the supply and demand functions for its most popular lamp are as follows:
$S ( p ) = 200 - 2 p + 0.00001 p ^ { 4 }$ and $D ( p ) = 1400 - 0.0006 p ^ { 3 }$, where $p$ is the price. Determine the price for which the supply equals the demand.
A) $\$ 96.24$
B) $\$ 100.24$
C) $\$ 93.24$
D) $\$ 99.24$

Question

Quizplus · Accepted Answer

To find the price where supply equals demand, set $S(p) = D(p)$ and solve for $p$. This gives $200 - 2p + 0.00001p^4 = 1400 - 0.0006p^3$. Solving this equation directly might be complex without a calculator or computational tool, but given the choices, the correct answer is found through approximation or computational methods, leading to $\$ 96.24$.

Solve the Problem S(p)=200−2p+0.00001p4S ( p ) = 200 - 2 p + 0.00001 p ^ { 4 }S(p)=200−2p+0.00001p4

Solve the Problem $S ( p ) = 200 - 2 p + 0.00001 p ^ { 4 }$