LazyBoy furniture distributes a computer worktable in three price differentiated markets (i = 1, 2 and 3). The annual demand for each market is linearly defined by the function Di=Ai-BiPi. The market parameters are A1=18000 B1= 121, A2=8700 B2=52, and A3=6000 B3= 30. The production cost a worktable is $28/unit. The maximum annual supply is 9200 units.

please solve:

i. Derive the optimal price and allocated supply quantity for each market. ii. What is the net supply chain profit? iii. If the company decides to close market #2, what is the lost profit? iv. For the three-market distribution, to what level should we increase the maximum annual supply to maximize profit