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=-2x^2+81x-359

The shape of the curve of the graph of the function of the company's profit

is a concave down parabola.

The maximum profit the company can make is approximately $461

Reasons:

The function for the profit the company makes, y = -2·x² + 81·x - 359

Where;

x = Selling price of each widget

Required:

The companies maximum profit given to the nearest dollar

Solution:

The value of the maximum profit is given by the maximum value of the

function, , the x-value of which is given when we have;

At the maximum value (profit), we have;

Therefore;

-4·x + 81 = 0

At the point of maximum profit, x = 20.25, therefore;

The maximum profit, = -2×20.25² + 81×20.25 - 359 = 461.125

The maximum profit to the nearest dollar, = $461

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The maximum profit that can make by the company  is $461.

Step-by-step explanation:

Given expression

y = the amount of profit

x= Number of widget.

We know that,

The maximum value of a function only when the value of

Here a= -2 and b=81

The profit of the company will maximum only when if they sell widget.

To find the maximum profit putting x= 20 in given expression.

   =$461

The maximum profit that can make by the company  is $461.

the first option is the answer.