Ghostbusters Co. provides the service of catching & destroying ghosts in a haunted town. In the following months of December, January and February, the company forecasts to receive 100, 300 and 200 calls, respectively, from its customers who want to get rid of the ghosts in their house. If the company responds to a call in the month the call is received (i.e. if the ghost related to that call is caught in the month the call is received) then the company will be paid $800 per call. If the company responds to the call with one month delay, they will be paid $700 per call, and if they respond to the call with 2-month delay, they will be paid $600 per call. It is required that the company responds to all the calls by the end of February (so a call that comes in February cannot be delayed). Each ghostbuster can catch up to 10 ghosts (i.e. responds to up to 10 calls) per month. The company pays to each ghostbuster $4,000 per month. At the beginning of December, there are 8 ghostbusters working for this company. At the beginning of each month, the company can hire new ghostbusters or lay off existing ones. The cost of hiring and training is $5,000 per every ghostbuster hired. The cost of laying off is $4,000 per every ghostbuster laid off. a) Formulate a mathematical programming model that will maximize the profit of Ghostbusters Co. b) Find the optimal solution using LINDO or Excel solver.