Tasty Inc. sells table salt to both retail grocery chains and commercial users (e.g., bakeries, snack food makers, etc.). The demand function for each of these markets is:

Retail grocery chains: P₁= 1808Q₁

Commercial users: P₂= 1004Q₂

where P₁and P₂are the prices charged and Q₁and Q₂are the quantities sold in the respective markets. Tasty's total cost function (which includes a "normal" return to the owners) for salt is:

TC = 50 + 20(Q₁+ Q₂)

(a) Determine Tasty's total profit function.

(b) Assuming that Tasty Inc. 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 Tasty's total profit under this condition?