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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 <em>x</em> items given by the function:
And the revenue for selling <em>x</em> 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 <em>P</em> equal 300 and solve for <em>x</em>. So:
Solve for <em>x</em>. 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 <em>or</em> 40 items.