This is all the information that was given.

4. From an old exam: (a) We are producing aluminum alloy to satisfy demand for the next five months. The demands are given below. The cost to produce also varies for each month as given in the same table. Monthly Demand and Production Costs Month 1 2 3 4 Demand 40 20 10 30 100 Cost per Unit $4 $4.2 $4.6 $5.6 $7.2 In each month, we can produce at most 50 units of aluminum. There is a $2 cost for holding a unit of aluminum in inventory for one month. In addition, to produce an alloy, you also need to setup the machine to operate for the month. It costs $500 to set up the machine for producing aluminum alloy. Formulate a mixed integer program to determine the optimal production schedule. Parameterize your model to allow for any number of months. You should give a value for any large constants in your formulation (e.g., you need to find the value for M, M2, etc.) (b) The aluminum alloy machine regularly needs to be shut down for maintenance. Up- date your model so that for any three consecutive months the aluminum alloy machine operates for 2 months, e.g., for months 1-3 it operates at most for 2 months, for months 2-4 it operates for at most 2 months, etc. 4. From an old exam: (a) We are producing aluminum alloy to satisfy demand for the next five months. The demands are given below. The cost to produce also varies for each month as given in the same table. Monthly Demand and Production Costs Month 1 2 3 4 Demand 40 20 10 30 100 Cost per Unit $4 $4.2 $4.6 $5.6 $7.2 In each month, we can produce at most 50 units of aluminum. There is a $2 cost for holding a unit of aluminum in inventory for one month. In addition, to produce an alloy, you also need to setup the machine to operate for the month. It costs $500 to set up the machine for producing aluminum alloy. Formulate a mixed integer program to determine the optimal production schedule. Parameterize your model to allow for any number of months. You should give a value for any large constants in your formulation (e.g., you need to find the value for M, M2, etc.) (b) The aluminum alloy machine regularly needs to be shut down for maintenance. Up- date your model so that for any three consecutive months the aluminum alloy machine operates for 2 months, e.g., for months 1-3 it operates at most for 2 months, for months 2-4 it operates for at most 2 months, etc