Problem 14-01 (Algorithmic) The RMC Corporation blends three raw materials to produoe two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of HZ ton of material 1 and 112 ton of material 3. A ton of solvent base is a mixture of 15 ton of material 1, 35 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, 16 tons; material 2, 18 tons; material 3, 12 tons. Management wants to achieve the Following P1 prioritv level goals: Goal 1: Produce at least 20 tons of fuel additive. Goal 2: Produce at least 15 tons of solvent base. Assume there are no other goals. a. Is it possible for management to achieve both P1 level goals given the constraints on the amounts of each material available? Amount needed to ) Raw Material Achieve Both P1 Goals 1 l: 2 l: 3 l: b. Treating the amounts of each material available as oonstraints, 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 oommon fraction. Let x; = the number of tons of 'Fuel additive produced X2 = the number of tons of solvent base prod uoed 61* = the amount by which the number of tons of fuel additive produced exoeeds the target value of 20 tons d1" = the amount by which the number of tons of fuel additive produoed is less than the target of 20 tons (12* = the amount by which the number of tons of solvent base produced exceeds the target value of 15 tons dz" = the amount by which the number of tons of solvent base is less than the target value of 15 tons