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 ton of material 3. A ton of solvent base is a mixture of ¹⁄2 ton of material 1, ¹⁄5 ton of material 2, and ³⁄10 ton of material 3. After deducting relevant costs, the profit 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 availability of the three raw materials. For the current production period, RMC has available the following quantities of each raw material:
|
Raw Material
|
Amount Available for Production
|
|
Material 1
|
20 tons
|
|
Material 2
|
5 tons
|
|
Material 3
|
21 tons
|
Assuming that RMC is interested in maximizing the total profit contribution, the problem formulation is shown here:
Max s.t.
40x1 +
²/5 x1 +
30x2
¹/2 x2 20
Material 1
¹/5 x2 5
³/5 x1 + ³/10 x2 21
x1, x2 > 0
Material 2
Material 3
where
x1 = tons of fuel additive produced
x2 = tons of solvent base produced
Solve the RMC problem using the simplex method. At each iteration, locate the basic feasible solution found by the simplex method on the graph of the feasible region.