Owens-Wheat uses two production lines to produce three types of fiberglass mat. The demand requirements (in tons) for each of the next four 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 five machines on line 1 and eight machines on line 2. Assume the per-ton cost of holding either product in inventory for one month is $5.
a. Determine a minimum cost production schedule for the next four months.
b. There is an important aspect of this situation that cannot be modeled by linear programming. What is it? (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?)
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