Use a graphing calculator to solve the nonlinear system. Give x- and y-coordinates to the nearest hundredth.
-A television manufacturing company has two different factories. The profit function for Factory I wl televisions are manufactured and sold is as follows:
$$P ( x ) = - 0.07 x ^ { 2 } + 25 x - 250$$
The profit function for Factory II when $x$ televisions are manufactured and sold is as follows:
$$P ( x ) = - 0.075 x ^ { 2 } + 35 x - 1500$$
For what number of televisions is the profit the same at both factories, and what is the profit?
A) 233 televisions; $\$ 2583.33$
B) 134 televisions; $\$ 1843$
C) 125 televisions; $\$ 1781.25$
D) 0 televisions; $\$ 0$ when x301)

Question

Quizplus · Accepted Answer

To find the number of televisions for which the profit is the same at both factories, set the two profit functions equal to each other and solve for $x$. This gives the equation $-0.07x^2 + 25x - 250 = -0.075x^2 + 35x - 1500$. Solving this equation, typically using a graphing calculator to find the intersection point(s) of the two parabolas represented by the profit functions, yields $x \approx 134$. Substituting $x = 134$ into either profit function gives the profit, which rounds to approximately $\$1843$.

Use a Graphing Calculator to Solve the Nonlinear System P(x)=−0.07x2+25x−250P ( x ) = - 0.07 x ^ { 2 } + 25 x - 250P(x)=−0.07x2+25x−250

Use a Graphing Calculator to Solve the Nonlinear System $P ( x ) = - 0.07 x ^ { 2 } + 25 x - 250$