Eli Orchid can manufacture its newest pharmacutical product in any of three processes.

One costs $14,000 per batch, requires 3 tons of one major ingredient and 1 ton of the other, and yields 2 tons of output product. The second process costs $30,000 per batch, requires 2 and 7 tons of the ingredients, respectively, and yields 5 tons of product. The third process costs $11,000 per batch, requires 9 and 2 tons of the ingredients, respectively, and yields 1 ton of product. Orchid wants to find the least costly way to produce at least 50 tons of the new product given that there are 75 tons of ingredient 1 and 60 tons of ingredient 2 on hand. (An optimization output appears in Table 6.7.)

(a) Briefly explain how this problem can be modeled by the LP min 14x1 + 30x2 + 11x3 s.t. 2x1 + 5x2 + 1x3 Ú 50 3x1 + 2x2 + 9x3 … 75 1x1 + 7x2 + 2x3 … 60 x1, x2, x3 Ú 0

(b) through

(d) as in Exercise 6-1.