The RMC Corporation blends three raw materials to produce two products: a fuel additive and a solvent base. Each
ton of fuel additive is a mixture of 0.4 ton of material 1 and 0.6 ton of material 3. A ton of solvent base is a mixture of 0.5 ton of material 1, 0.2 ton of material 2, and 0.3 ton of material 3. RMC's production is constrained by a limited availability of the three raw materials. For the current production period, RMC has the following quantities of each raw material: material 1, 20 tons; material 2, 5 tons; material 3, 21 tons. Management wants to achieve the following goals (assume there are NO other goals):
Goal 1: Produce at least 30 tons of fuel additive.
Goal 2: Produce at least 15 tons of solvent base.
Treating the amounts of each material available as constraints, formulate a goal programming model (identify and define decision variables, objective function and constraints) to determine the optimal mix. Assume that goal 1 is more important than goal 2.