Consolidated Sugar Company sells granulated sugar to both retail grocery chains and commercial users (e.g., bakeries, candy makers, etc.). The demand function for each of these markets is:
Retail grocery chains: P₁ = 90 – 4q₁   
Commercial users:      P₂ = 50 – 2q₂

where P₁ and P₂ are the prices charged and q₁ and q₂ are the quantities sold in the respective markets. Consolidated's total cost function (which includes a "normal" return to the owners) for granulated sugar is

T_C = 25 + 10(q₁ + q₂)
(a) Determine Consolidated's total profit function.

(b) Assuming that Consolidated is effectively able to charge different prices in the two markets, what are the profit-maximizing price and output levels for the product in the two markets? What is Consolidated's total profit under this condition?
(c) Assuming that Consolidated is required to charge the same price in each market, what are the profit-maximizing price and output levels? What is Consolidated's total profit under this condition?