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 $

x = $36 , y = $ 838

Step-by-step 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:

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:

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

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:

The maximum profit would be y = $838

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