Question

Photon Lighting Company determines that the supply and demand functions for its most popular lamp are as follows: S(p) = 400 - 4p + 0.00002p4 and D(p) = 2800 - 0.0012p3, where p is the price. Determine the price for which the supply equals the demand.

A) $93.24
B) $100.24
C) $96.24
D) $99.24

Answer 1

Answer: The correct answer is (C).

Explanation:

Supply function:

$S(p)=400-4p+0.00002p^4$

Demand function:

$D(p)=2800-0.0012p^3$

S(p)=D(p), price for which supply is equal to demand:

$S(p)=D(p)=400-4p+0.00002p^4=2800-0.0012p^3$

After solving this above equation graphically, we will get the values of p.

1) p =96.236

2) p=( -118.258)

We will reject the negative value of p.

So, the value of p that price for which the supply equals the demand is $ 96.236 $\approx$ $96.24. Hence, the correct answer is option (C).

Answer 2

Answer:

Price equals $96.24

Explanation:

It is given that,

The supply function is given by, $S(p)=400-4p+0.00002p^4$

The demand function is given by, $D(p)=2800-0.0012p^3$

We have to find the price for which the supply equals to the demand.

$S(p)=D(p)$

$400-4p+0.00002p^4=2800-0.0012p^3$

After solving above equation we get :

So, it is clear from the attached graph that p = 96.24 and q = -118.26

So, the correct option is (c) " $96.24 ".