1. The cost to manufacture x units of a product is 15000 + 40x + 0.02x². The revenue from the sale of these products is 100x - .01x². Find the level of sales that will maximize profit. 2. A manufacturer makes a product at a cost of $12/unit. He estimates demand will be 50 - p units when the price is p dollars (for example, at $10, he can sell 40 units). Find the cost, revenue and profit equations, as functions of price p. Then find the price that maximizes the profit. 3. A manufacturer builds q items at a cost of 6000 + 5q + 0.01q². To sell q items, the price needs to be 20 - q/4 . (So these are your C and p functions.) Find the quantity that will maximize profit.
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To find the level of sales that will maximize profit, we need to first find the profit equation. Profit = Revenue - Cost. Revenue = 100xO1x Cost = 15000 + 4Ox + 0.02x Profit = 100xO1x - (15000 + 4Ox + 0.02x) To maximize profit, we need to find the Show more…
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