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 = 800 + 53Q, Q = Q₁ + Q₂

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

Q₁ = 73 - P₁ and 0.5Q₂ = 100 - P₂

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

c) If James decides to make a total of 51rolls and pies per day and charges different prices as above (that is, ? ? ), how many of rolls and pies each

should he make in order to maximize the profit of a particular day? Estimate the increase in maximum profit which results when the total number of rolls and pies per day (51) is increased to 52 [assume second-order conditions are satisfied].