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

In order to add the fractions, we need to create complex fractions with a Least Common Denominator (LCD). 

The LCD between 9 and 2 is 18

3 1/2 = 3(18/18) + 9/18 = 54/18 + 9/18 = 63/18
3/9 = 6/18

So now we can solve...

3 1/2 + 3/9 is the same as 63/18 + 6/18 = 69/18 = 3 5/6 which is none of the given answers.