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−0.4x2. How many items must be sold to obtain a weekly profit of $300?

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.