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total profit functions

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Philips Industries manufactures a certain product that can be sold directly to retail outlets or to the Superior Company for further processing and eventual sale as a completely different product. The demand function for each of these markets is

Retail Outlets: P1 = 60 - 2Q1

Superior Company: P2 = 40 - Q2

where P1 and P2 are the prices charged and Q1 and Q2 are the quantities sold in the respective markets. Phillip's total cost function for the manufacture of this product is

TC = 10 + 8(Q1 + Q2)

a. Determine Phillip's total profit functions.
b. What are the profit-maximizing price and output levels for the product in the two markets?
c. At these levels of output, calculate the marginal revenue in each market.

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Solution Preview

a. Determine Phillip's total profit functions.

Total Revenue from Retail outlets=Price*Quantity=(60-2Q1)*Q1

Total Revenue from Superior Company=Price*Quantity=(40-Q2)*Q2

Total Cost, TC=10+8(Q1+Q2)

Profit=Total Revenue-Total Cost

Solution Summary

The total profit functions are scrutinized.