Which of the following is NOT a way to express the formula for profit? Question 8 options: Profit = Revenue - Cost pi = R(Q) - C(Q) pi = [P(Q) imes Q] - [C(Q) imes Q] pi = [P(Q) imes Q] - C(Q)
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Step 1: The formula for profit can be expressed as Profit = Revenue - Cost. Show more…
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The revenue from selling q items is R(q) = 500q - q^2 and the total cost is C(q) = 150 + 10q. Write a function that gives the total profit earned and find the quantity which maximizes the profit.
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Let $C(q)$ represent the cost, $R(q)$ the revenue, and $\pi(q)$ the total profit, in dollars, of producing $q$ items. (a) If $C^{\prime}(50)=75$ and $R^{\prime}(50)=84,$ approximately how much profit is earned by the $51^{\text {st }}$ item? (b) If $C^{\prime}(90)=71$ and $R^{\prime}(90)=68,$ approximately how much profit is earned by the $91^{\text {st }}$ item? (c) If $\pi(q)$ is a maximum when $q=78,$ how do you think $C^{\prime}(78)$ and $R^{\prime}(78)$ compare? Explain.
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