39.9k views
1 vote
The company sells widgets, and the relationship between the selling price of each widget, x, and the resulting profit, y, is given by the equation y = -8x^2 + 456x - 2704. What price should the widgets be sold for, rounded to the nearest cent, to maximize the company's profit?

A) $28.50
B) $28.75
C) $29.00
D) $29.25

User SpellingD
by
7.5k points

1 Answer

3 votes

Final answer:

To maximize the company's profit, the widgets should be sold for B) $28.50.

Step-by-step explanation:

To find the price that should be sold for widgets to maximize the company's profit, we need to find the vertex of the quadratic equation y = -8x^2 + 456x - 2704.

The x-coordinate of the vertex, which represents the price, can be found using the formula x = -b / (2a), where a, b, and c are the coefficients of the quadratic equation.

In this case, a = -8 and b = 456.

Plugging these values into the formula, we get x = -456 / (2 * -8) = $28.50.

Therefore, the widgets should be sold for $28.50, rounded to the nearest cent, to maximize the company's profit.

User NateLillie
by
8.8k points

Related questions

asked Aug 14, 2021 88.3k views
Guyskk asked Aug 14, 2021
by Guyskk
8.6k points
2 answers
4 votes
88.3k views
asked Jul 12, 2023 219k views
Elise Chant asked Jul 12, 2023
by Elise Chant
7.3k points
1 answer
0 votes
219k views
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.