8 A company produces six products in the following fashion. Each unit of raw material purchased yields four units of product 1, two units of product 2, and one unit of product 3. Up to 1,200 units of product 1 can be sold, and up to 300 units of product 2 can be sold. Each unit of product 1 can be sold or processed further. Each unit of product 1 that is processed yields a unit of product 4.

Demand for products 3 and 4 is unlimited. Each unit of product 2 can be sold or processed further. Each unit of product 2 that is processed further yields 0.8 unit of product 5 and 0.3 unit of product 6. Up to 1,000 units of product 5 can be sold, and up to 800 units of product 6 can be sold.

Up to 3,000 units of raw material can be purchased at $6 per unit. Leftover units of products 5 and 6 must be destroyed.

It costs $4 to destroy each leftover unit of product 5 and $3

to destroy each leftover unit of product 6. Ignoring raw material purchase costs, the per-unit sales price and production costs for each product are shown in Table 24.
Formulate an LP whose solution will yield a profitmaximizing production schedule.

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Product 1 Sales Price ($) Production Cost (S) 794 23456 442155 4 3 20 20 35