Question

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. y=-x^2+78x-543

Answer 1

The maximum amount of profit the company can make is $978 (to the nearest dollar).

Step-by-step explanation:

The company's profit function is given by the equation y = -x^2 + 78x - 543. To find the maximum amount of profit, we need to determine the value of x that corresponds to the vertex of the parabolic graph represented by this equation. The x-coordinate of the vertex can be found using the formula x = -b/(2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = -1, b = 78, and c = -543. Plugging these values into the formula, we get x = -78/(2*(-1)) = 39. Substitute this value of x back into the profit function to find the maximum profit:

y = -(39^2) + 78(39) - 543 = -1521 + 3042 - 543 = 978

Hence, the maximum profit the company can make is $978 (to the nearest dollar).