Suppose that you own the only company in the market to produce a certain product, and...

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Suppose that you own the only company in the market to produce a certain product, and therefore you can determine the market price P dollars for each unit. Due to government regulations, the price of each unit must be in the range 10 < P < 30. The market demand Q is a function of P given by Q=1000-P-p. (1) Derive the total revenue function, denote it as f(P), and define its domain (no explana- tion is needed). (2) Compute the maximum value of the total revenue function. You may assume that the maximum point exists (round your result to two decimal places). (3) Is f(P) a strictly concave or a strictly convex function? Carefully explain your answer. (4) Calculate the price elasticity of the total revenue, that is, Elpf(P), at P = 15. Provide a brief interpretation of the computed price elasticity, in the context of this example (round Activate your result to two decimal places). Go to Sett Suppose that you own the only company in the market to produce a certain product, and therefore you can determine the market price P dollars for each unit. Due to government regulations, the price of each unit must be in the range 10 < P < 30. The market demand Q is a function of P given by Q=1000-P-p. (1) Derive the total revenue function, denote it as f(P), and define its domain (no explana- tion is needed). (2) Compute the maximum value of the total revenue function. You may assume that the maximum point exists (round your result to two decimal places). (3) Is f(P) a strictly concave or a strictly convex function? Carefully explain your answer. (4) Calculate the price elasticity of the total revenue, that is, Elpf(P), at P = 15. Provide a brief interpretation of the computed price elasticity, in the context of this example (round Activate your result to two decimal places). Go to Sett