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Answer :
Final answer:
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.
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