Quadratic Polynomial Profit Problem...please help

Question

For a certain company, the cost for producing x items is 55x+300 and the revenue for selling x items is 95x−0.5x2.

A) set up an expression for the profit from producing and selling x items.

B) find two values of x that will create a profit of $50

C)is it possible for the company to make a profit of $2500

Answer 1

Profit = Revenue - cost = 95x - x² - 55x - 300 = -x² +45x - 300

For b you need to find x, so that -x² + 45x - 300 = 50, or -x² + 45x - 350 = 0

You can solve this with the quadratic formula, or plot y=-x² + 45x - 300, and y = 50 on Desmos and read off the x coordinates where the lines intersect.

(c). -x² + 45x - 300 is facing down (as a <0)

x coordinate of vertex is at -b/2a = -45/-2 = 45/2

profit there is 206.25. This is the maximum possible profit. So the answer is no.