Solve the problem.
-Suppose the supply function of a certain item is given by $S(x)=4 x+2$ and the demand function is $D(x)=14-x^{2}$. Find the producer's surplus.
A) 8
B) $\frac{8}{3}$
C) 16
D) $\frac{16}{3}$

Question

Quizplus · Accepted Answer

The producer's surplus is the area above the supply curve and below the demand curve. The points of intersection of the two curves are found by solving the equation $S(x)=D(x)$:$$4x+2=14-x^2$$$$x^2+4x-12=0$$$$(x+6)(x-2)=0$$$$x=-6,2$$The producer's surplus is the area of the triangle with vertices $(2,6)$, $(0,2)$, and $(-6,0)$:$$\frac{1}{2}(2)(6)=6$$Therefore, the producer's surplus is 6.

Solve the Problem S(x)=4x+2S(x)=4 x+2S(x)=4x+2 And the Demand Function Is D(x)=14−x2D(x)=14-x^{2}D(x)=14−x2 Find the Producer's Surplus

Solve the Problem $S(x)=4 x+2$ And the Demand Function Is $D(x)=14-x^{2}$ Find the Producer's Surplus