a company sells widgets. the amount of profit, y, made by the company, is related to the selling price of…

a company sells widgets. the amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.\n\n$y = - 18x^{2}+968x - 7150$

a company sells widgets. the amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation. using this equation, find out the maximum amount of profit the company can make, to the nearest dollar.\n\n$y = - 18x^{2}+968x - 7150$

Answer

Explanation:

Step1: Find the x - coordinate of the vertex

For a quadratic function (y = ax^{2}+bx + c), the (x) - coordinate of the vertex is given by (x=-\frac{b}{2a}). Here, (a=-18) and (b = 968). [x=-\frac{968}{2\times(-18)}=\frac{968}{36}\approx26.89]

Step2: Substitute (x) into the profit function

Substitute (x = \frac{968}{36}) into (y=-18x^{2}+968x - 7150). [ \begin{align*} y&=-18\times(\frac{968}{36})^{2}+968\times\frac{968}{36}-7150\ &=-18\times\frac{937024}{1296}+\frac{937024}{36}-7150\ &=-\frac{16866432}{1296}+\frac{31234136}{1296}-7150\ &=\frac{- 16866432 + 31234136}{1296}-7150\ &=\frac{14367704}{1296}-7150\ &\approx11086.2 - 7150\ &=3936.2 \end{align*} ]

Answer:

(3936)