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. y=-x^2+72x-458 We need to sell each widget at $ ___ in order to make a maximum profit of $ ____

Answer 1

x = $36 , y = $ 838

Explanation:

Solution:-

The company makes a profit of $y by selling widgets at a price of $x. The profit model is represented by a parabola ( quadratic ) equation as follows:

`y = -x^2 + 72x -458`

We are to determine the profit maximizing selling price ( x ) and the corresponding maximum profit ( y ).

From the properties of a parabola equation of the form:

`y = ax^2 + bx + c`

The vertex ( turning point ) or maximum/minimum point is given as:

`x = -(b)/(2a) \\\\x = -(72)/(-2) = 36`

The profit maximizing selling price of widgets would be x = $36. To determine the corresponding profit ( y ) we will plug in x = 36 in the given quadratic model as follows:

`y ( 36 ) = - ( 36 )^2 + 72 ( 36 ) - 458\\\\y ( 36 ) = -1296 + 2592 - 458\\\\y ( 36 ) = 838`

The maximum profit would be y = $838