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 how much the widgets would have to be sold for, to the nearest cent, in order for the company to break even. Only enter one possible price. y=-8x^2+348x-1705

Answer 1

Price of widget to break even= $37.9

Explanation:

We are told that the equation representing the amount of profit, y, made by the company, in relation to the selling price of each widget, x is;

y = -8x² + 348x - 1705

Now, the company will break even when it has made no profit. That is when, y = 0

Thus;

0 = -8x² + 348x - 1705

Rearranging,

8x² - 348x + 1705 = 0

Using quadratic formula ;

x = [-b ± √(b² - 4ac)]/2a

x = [-8 ± √(-348² - 4•1•1705)]/(2 x 8)

x = $5.63 or $37.87

We'll use $37.87 because it is the highest price for which no profit is made, and higher price means that we could sell least number of products to earn a certain amount of money.

We are told to approximate to nearest cent. Thus,

Price of widget = $37.87 ≈ $37.9