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Question: james mainly sells confectionery items newspapers magazines and cigarettes in...

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James mainly sells confectionery items, newspapers, magazines, and cigarettes in his convenience store. Noting his small business is not thriving, he thought of selling hot pies and rolls too.

Suppose the total cost function for rolls and pies is,

TC = 900 + 50Q,    Q =Q1 +Q2

where Q1  and   Q2 denote the quantities of rolls and pies respectfully. If P1 and P2 denote the corresponding prices, the inverse demand equations are. 

Q1 = 70 - P1 and 0.5Q2 = 100 - P2

a) If James decides to charge the same price for rolls and pies per day (that is, P1 = P2), how many rolls and pies in total should he make in order to maximize the profit of a particular day?

b) If James decides to charge different prices as above for rolls and pies per day (that is, P1 ≠ P2), how many rolls and pies should he make in order to maximize the profit of a particular day?

c) Which of the above options (a) or (b) is more profitable? Provide the rationale for your answer.

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