Answer
The company must be able to sell $more$ $than$ $6,250$ tapes in order to be able to make a profit.
Work Step by Step
To solve this exercise, we must first model the expenses of manufacture and the price of selling the tapes: $$Expenses= 10,000 + 0.4T$$ $$Price= 2T$$ where $T$ represents the amount of tapes sold in a week. Since we're interested in identifying the amount of tapes sold needed to make a profit, this is the same as saying that we need the amount of money made in $Price$ to be larger than the costs modeled in $Expenses$: $$Price \gt Expenses$$ $$2T \gt 10,000 + 0.4T$$ where by, we solve for $T$: $$2T - 0.4T \gt 10,000$$ $$1.6T \gt 10,000$$ $$T \gt 6,250$$ This means that the company must be able to sell $more$ $than$ $6,250$ tapes in order to be able to make a profit.
