RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3 . A ton of solvent base is a mixture of 12 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3 . After deducting relevant costs, the profit(_t contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC's production is constrained by a limited ( of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Assuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of tons of fuel additive and S is the number of tons of solvent base.) (a) What is the linear programming model for this problem that maximizes profit (in dollars)? Max : s.t.Material 1 : Material 2 : Material 3:F,S0 (b) Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced? (F,S)=(C) What is the projected total profit contribution (in dollars)? $: (c) Is there any unused material? If so, how much (in tons)? (If there is no unused material, enter 0 .) Material 1: tons Material 2 : tons Material 3: tons (d) Are any of the constraints redundant? If so, which ones? (Select all that apply.) A, Material 1 constraint B, Material 2 constraint C, Material 3 constraint D, No redundant constraints RMC, Inc., is a small firm that produces a variety of chemical products. In a particular production process, three raw materials are blended (mixed together) to produce two products: a fuel additive and a solvent base. Each ton of fuel additive is a mixture of 2/5 ton of material 1 and 3/5 of material 3 . A ton of solvent base is a mixture of 12 ton of material 1, 1/5 ton of material 2, and 3/10 ton of material 3 . After deducting relevant costs, the profit(_t contribution is $40 for every ton of fuel additive produced and $30 for every ton of solvent base produced. RMC's production is constrained by a limited ( of the three raw materials. For the current production period, RMC has available the following quantities of each raw material: Assuming that RMC is interested in maximizing the total profit contribution, answer the following. (Assume F is the number of tons of fuel additive and S is the number of tons of solvent base.) (a) What is the linear programming model for this problem that maximizes profit (in dollars)? Max : s.t.Material 1 : Material 2 : Material 3:F,S0 (b) Find the optimal solution using the graphical solution procedure. How many tons of each product should be produced? (F,S)=(C) What is the projected total profit contribution (in dollars)? $: (c) Is there any unused material? If so, how much (in tons)? (If there is no unused material, enter 0 .) Material 1: tons Material 2 : tons Material 3: tons (d) Are any of the constraints redundant? If so, which ones? (Select all that apply.) A, Material 1 constraint B, Material 2 constraint C, Material 3 constraint D, No redundant constraints
