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$y=-x^{2}+77x - 303$

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$y=-x^{2}+77x - 303$

Answer

Explanation:

Step1: Identify the coefficients

For the quadratic function (y = ax^{2}+bx + c), in (y=-x^{2}+77x - 303), (a=-1), (b = 77), (c=-303).

Step2: Find the x - coordinate of the vertex

The formula for the x - coordinate of the vertex of a quadratic function (y = ax^{2}+bx + c) is (x=-\frac{b}{2a}). Substitute (a=-1) and (b = 77) into the formula: (x=-\frac{77}{2\times(-1)}=\frac{77}{2}=38.5)

Step3: Find the y - coordinate of the vertex

Substitute (x = 38.5) into the equation (y=-x^{2}+77x - 303) (y=-(38.5)^{2}+77\times38.5-303) First, calculate ((38.5)^{2}=38.5\times38.5 = 1482.25) Then (77\times38.5=77\times(38 + 0.5)=77\times38+77\times0.5=2926+38.5 = 2964.5) (y=-1482.25+2964.5-303) (y=( - 1482.25+2964.5)-303) (y = 1482.25-303) (y=1179.25\approx1179)

Answer:

(1179)