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The total cost (in dollars) for a company to manufacture and sell x items per week is C=40x+180, whereas the revenue brought in by selling a
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The total cost (in dollars) for a company to manufacture and sell x items per week is C=40x+180, whereas the revenue brought in by selling all x items is R=68x−0.4×2. How many items must be sold to obtain a weekly profit of $300?
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Mathematics
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2021-08-31T05:46:58+00:00
2021-08-31T05:46:58+00:00 1 Answers
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Answer:
The company needs to sell either 30 or 40 items.
Step-by-step explanation:
We are given that the cost for selling x items given by the function:
And the revenue for selling x items is given by:
The profit function is the cost function subtracted from the revenue function:
Substitute and simplify:
To find how many items must be sold in order to obtain a weekly profit of $300, we can let P equal 300 and solve for x. So:
Solve for x. Subtract 300 from both sides:
We can divide both sides by -0.4:
Factor:
Zero Product Property:
Solve for each case:
So, in order to obtain a weekly profit of $300, the company need to sell either 30 or 40 items.