Problem 14-01 (Algorithmic) 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 1/2 ton of material 1 and 1/2 ton of material 3. A ton of solvent base is a mixture of 2/5 ton of material 1, 2/5 ton of material 2, and 1/5 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, 16 tons; material 3, 15 tons. Management wants to achieve the following P priority level goals: Goal 1: Produce at least 35 tons of fuel additive. Goal 2: Produce at least 25 tons of solvent base. Assume there are no other goals. a. Is it possible for management to achieve both P level goals given the constraints on the amounts of each material available? Explain. Amount needed to Raw Material Achieve Both P Goals 1 2 3 Since there are only 20 tons of Material 1 and 15 tons of Material 3 available, it is b. Treating the amounts of each material available as constraints, formulate a goal programming model to determine the optimal product mix. Assume that both P priority level goals are equally important to management. If you don't need the variable in the model, enter "0". If you need a negative number, enter minus sign with it. If necessary, enter the numbers as a common fraction. Let x1 = the number of tons of fuel additive produced x2 = the number of tons of solvent base produced d* = the amount by which the number of tons of fuel additive produced exceeds the target value of 35 tons di = the amount by which the number of tons of fuel additive produced is less than the target of 35 tons d+ = the amount by which the number of tons of solvent base produced exceeds the target value of 25 tons d the amount by which the number of tons of solvent base less than the target value of 25 tons Min di |+ d s.t. + Material 1 X1 + Material 2 Material 3. +