The lowest weekly total cost, operating plants 1 and 3 with 2closed, is $217,430. This is $3,300 per week ($171,600 per year)or 1.5% less than the next most economical solution, operating allthree plants. Closing a plant without expanding the capacity of theremaining plants means unemployment. The optimum solution,using plants 1 and 3, indicates overtime production of 4,000 unitsat plant 1 and 0 overtime at plant 3. The all-plant optima have nouse of overtime and include substantial idle regular time capacity:11,000 units (55%) in plant 2 and either 5,000 units in plant 1(19% of capacity) or 5,000 in plant 3 (20% of capacity). The idledcapacity versus unemployment question is an interesting, non-quantitative aspect of the case and could lead to a discussion of theforecasts for the housing market and thus the plant’s product.The optimum producing and shipping pattern is
There are three alternative optimal producing and shipping pat-terns, where R.T = regular time, O.T.= overtime, and W= warehouse. Getting the solution manually should not be attempted usingthe northwest corner rule. It will take eight tableaux to do the “allplants” conﬁguration, with degeneracy appearing in the seventhtableau; the “1 and 2” conﬁguration takes ﬁve tableaux; and so on.It is strongly suggested that software be used.