Question

If a manufacturer can produce a certain item for $7 and sell the item for x...

If a manufacturer can produce a certain item for $7 and sell the item for x dollars, the profit per item will be x - 7 dollars. If it is then estimated that consumers will buy 25 - x items per month, the total profit will be:

Total Profit = (number of items sold)(profit per item) = (25 - x)(x - 7)

Use this information to create a quadratic equation. Then graph your equation, and based on the graph, what value of x will create the greatest profits? What will that profit be? What part of the graph did you use to find this information? Explain how this process could be useful in other scenarios.

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