A company's profit is described by the equation P(x)=-5x^2+300x+15,000 Where x is the price in dollars that the company charges for its product. What should the company charge for the product to generate the maximum profit?A)$20B)$30C$50D$60
Accepted Solution
A:
P(x)=-5x^2+300x+15,000 is the equation of a parabola and represents profit. Its graph opens down. Our job is to find the x-coordinate of the vertex (which is the x-coord of the maximum profit) and then the corresponding y-value.
The formula x = -b / (2a) will produce that x-coordinate:
-(300) x = ------------ = 30 2(-5)
When x=30 units, y = profit = -5(30)^2 + 300(30) + 15000 = $19500 (answer)