Owens-Wheat uses 2 production lines to produce 3 types of fiberglass mat. The demand requirements (in tons) for each of the next 4 months are shown in the file P04_115.xlsx. If it were dedicated...

Owens-Wheat uses 2 production lines to produce 3 types of fiberglass mat. The demand requirements (in tons) for each of the next 4 months are shown in the file P04_115.xlsx. If it were dedicated entirely to the production of one product, a line 1 machine could produce either 20 tons of type 1 mat or 30 tons of type 2 mat during a month. Similarly, a line 2 machine could produce either 25 tons of type 2 mat or 28 tons of type 3 mat. It costs $5000 per month to operate a machine on line 1 and $5500 per month to operate a machine on line 2. A cost of $2000 is incurred each time a new machine is purchased, and a cost of $1000 is incurred if a machine is retired from service. At the end of each month, Owens would like to have at least 50 tons of each product in inventory. At the beginning of month 1, Owens has 5 machines on line 1 and 8 machines on line 2. Assume the perton cost of holding either product in inventory for 1 month is $5.

a. Determine a minimum cost production schedule for the next 4 months.

b. There is an important aspect of this situation that cannot be modeled by linear programming. What is it? (Hint: If Owens makes product 1 and product 2 on line 1 during a month, is this as efficient as making just product 1 on line 1?)