Cohen Chemicals, Inc., produces two types of photo-developing fluids. The first, a black-and-white picture chemical, costs Cohen $2,500 per ton to produce. The second, a color photo chemical, costs $3,000 per ton.

Based on an analysis of current inventory levels and outstanding orders, Cohen’s production manager has specified that at least 30 tons of the black-and-white chemical and at least 20 tons of the color chemical must be produced during the next month. In addition, the manager notes that an existing inventory of a highly perishable raw material needed in both chemicals must be used within 30 days. To avoid wasting the expensive raw material, Cohen must produce a total of at least 60 tons of the photo chemicals in the next month.

APPROACH c Formulate this information as a minimization LP problem Let:
X1 = number of tons of black@and@white photo chemical produced X2 = number of tons of color photo chemical produced Objective: Minimize cost = +2,500X1 + +3,000X2 Subject to:
X1 Ú 30 tons of black@and@white chemical X2 Ú 20 tons of color chemical X1 + X2 Ú 60 tons total X1, X2 Ú 0 nonnegativity requirements