Acompany 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=-3x^2+155x-1148

The maximum profit is $854

Profit is the difference between the revenue and the cost price of an item. It is given by:

Profit = selling price - cost price

Since x represent the profit made by the company, is related to the selling price of each widget, x and it is given by the formula:

y = -3x² + 155x - 1148

At maximum profit, dy/dx = 0, hence:

dy/dx = -6x + 155

0 = -6x + 155

6x = 155

x = 25.83

The maximum profit is at gotten when the selling price of each widget is 25.83. Hence:

y = -3(25.83)² - 155(25.83) - 1148

y = $854

Therefore the maximum profit is $854

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The maximum amount of profit the company can make is $854.08

Step-by-step explanation:

Let

x ----> the selling price of each widget

y ---> the amount of profit

we have

This is the equation of a vertical parabola open downward (because the leading coefficient is negative)

The vertex represent a maximum

so

The y-coordinate of the vertex represent  the maximum amount of profit the company can make

using a graphing tool

Find out the vertex of the quadratic equation

The vertex is the point (25.83,854.08)

see the attached figure

The y-coordinate of the vertex is 854.08

therefore

The maximum amount of profit the company can make is $854.08