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A company wishes to predict the production rates for the next six months for a perishable product. The expected demand is 30, 80, 60, 50 , 80 and 100 units for months 1,: : :, 6, respectively. Since the product is perishable, it is not stored from month to month.

The loss per unit not sold is $8 and the loss per unit short is $5. Given the nature of the production process, the production output must be maintained at some linear function over the time period.

(a) Formulate this problem and solve a model to minimize the total costs.

(b) Reformulate and solve if desire to minimize the maximum loss in any one month.

(c) Compare the results obtained in part b with that which would be achieved using the least squares method to fit the production rate response.