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

Question

2 years ago

9

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 what price the widgets should be sold for, to the nearest cent, for the company to make the maximum profit. y = -5x² + 194x - 990

Mathematics

1 answer:

Anastasy [175] · Answer 1 · 2022-10-06T20:26:53+03:00

Anastasy [175]2 years ago

8 0

Answer: 19.4

Step-by-step explanation:

Given

Profit is given in terms of the selling price

$y=-5x^2+194x-900$

to get the maximum price, differentiate y w.r.t x

$\frac{\mathrm{d} y}{\mathrm{d} x}=-5\times 2x+194$

Put $\frac{\mathrm{d} y}{\mathrm{d} x}=0$ to get maximum value

$10x=194\\x=19.4$

Thus, the company must sell it at 19.4