Consider the Wyndor Glass Co. problem described in Sec. 3.1 (see Table 3.1). Suppose that decisions have been made to discontinue additional products in the future and to initiate other new products. Therefore, for the two products being analyzed, the number of hours of production time available per week in each of the three plants will be different than shown in Table 3.1 after the first year. Furthermore, the profit per batch (exclusive of storage costs) that can be realized from the sale of these two products will vary from year to year as market conditions change. Therefore, it may be worthwhile to store some of the units produced in 1 year for sale in a later year. The storage costs involved would be approximately $2,000 per batch for either product.
The relevant data for the next three years are summarized next.

The production time per batch used by each product remains the same for each year as shown in Table 3.1. The objective is to determine how much of each product to produce in each year and what portion to store for sale in each subsequent year to maximize the total profit over the three years.
(a) Formulate this problem as a multitime period linear programming problem.
(b) Construct the corresponding table of constraint coefficients having the dual angular structure shown in Table 23.9.

Transcribed Image Text:

Hours/Week Available in Year 2 4 2 12 318 Plant 10 15 $5,000 $8,000 12 24 Profit per batch, Produt 3,000 $4,000 Profit per batch, Product 2 $5,000 $4,000