A small-appliance manufacturer finds that the profit P (in dollars) generated by producing x microwave ovens per week is given by the formula P = (1/10) * x(300 - x) provided that 0 ≤ x ≤ 200. How many ovens must be manufactured in a given week to generate a profit of $2240? Smaller value ovens or larger value ovens?
a) 80 ovens
b) 120 ovens
c) 160 ovens
d) 200 ovens

To generate a profit of $2240, the small-appliance manufacturer must produce 160 microwave ovens per week, which is the larger value option hence, answer is c) 160 ovens.

Explanation:

To find how many ovens must be manufactured in a given week to generate a profit of $2240, we can set the profit equation P = (1/10) * x(300 - x) equal to 2240 and solve for x. We get:

2240 = (1/10) * x(300 - x)

22400 = x(300 - x)

We can solve this quadratic equation by expanding and rearranging the terms:

0 = x^2 - 300x + 22400

Using the quadratic formula, x = [-(-300) "+" sqrt((-300)^2-4(1)(22400))]/(2(1)) or
x = [-(-300) "-" sqrt((-300)^2-4(1)(22400))]/(2(1))

This simplifies to x = 160 or x = 140. Since only one of these values is provided in the multiple-choice options, the correct answer is:

a) 160 ovens

By producing 160 ovens, the manufacturer will generate a profit of $2240. This is the larger value among the given options.