Question

**The average revenue for product Q is given by AR = 200 – 3.5Q and the total cost of Q**

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**STC = 500-6Q+3Q^2 Note: this is not a typical cubic function**

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**a. Find the price function and then the TR function. Hint: another name for price is average revenue (AR).**

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**b. Write the MR and MC functions below. Remember: MR = dTR/dQ and MC = dSTC/dQ. **

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**c. What positive value of Q will maximize total profit? Remember, letting MR = MC signals the objective of total profit maximization. Solve MR = MC for Q. The value of Q you get should not be zero or negative)?**

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**d. Use the price function found in (a) to determine the price per unit that will need to be charged at the Q found in (c). This will be the price you should ask for the total profit maximizing quantity.**

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**e. What total profit will result from selling the quantity found in (c) at the price found in (d)? Hint: the profit function is found as TR – STC.**

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**f. At what level of Q is revenue maximized? Remember, let MR = 0 and solve for Q. MR = 0 signals the objective of maximizing revenue.**

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**g. At what level of Q is average profit per unit maximized? Hint: the average profit function is the total profit function found in (e) divided by Q. To find the level of Q that maximizes average profit, find the first derivative of average profit, set this derivative equal to zero and solve for Q.**

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**h. What price per unit should be charged at the quantity found in (g)? Simply plug the Q you got in (g) into the same price function you found in (a) and also used in (d).**

Economics