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. Using this equation, find out the maximum amount of profit
the company can make, to the nearest dollar.
y = -4x^2 + 183x – 1247

Answer 1

846.06 units

Explanation:

The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the given equation as follows :

`y = -4x^2 + 183x- 1247` ...(1)

We need to find out the maximum amount of profit the company can make.

For maximum profit put dy/dx = 0

So,

`(d)/(dx)(-4x^2 + 183x- 1247)=0\\\\-8x+183=0\\\\x=(183)/(8)\\\\x=22.87`

Put x = 22.87 in equation (1). So,

`y = -4(22.87)^2 + 183(22.87)- 1247\\\\=846.06`

So, the maximum profit is 846.06 units.