Hi, I've been stuck on this problem for a while and would love some help. Thanks!

Problem 14-01 (Also rlthmlc) 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 HZ ton of material 1 and Liz ton of material 3. A ton of solvent base is a mixture of 115 ton of material 1, 3,1'5 ton of material 2, and HS ton of material 3. RMC's production is constrained by a limited availability of the three rawI 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 priority 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 P; level goals given the constraints on the amounts of each material available? Arnou nt needed to Raw Material Achieve Both Pl Goals 1 g 2 :l 3 :l b. Treating the amounts of each material available as constraints, formulate a goal programming model to determine the optimal product mix. Assume that both P1 priority level goals are equally important to management. If you don't need the variable in the model, enter '0". If you need 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 produced df = the amount by which the number of tons of fuel additive produced exceeds the target value of 20 tons d1" = the amount by which the number of tons of fuel additlve produced is less than the target of 20 tons df = the amount by which the number of tons of solvent base produced exceeds the target value of 15 tons d2" = the amount by which the number of tons of solvent base ls less than the target value of 15 tons