Recall the RMC problem (Chapter 2, Problem 12). Letting:
F = kilos of fuel additive
S = kilos of solvent base
leads to the formulation:
Max 40F + 30S
s:t
Use the graphical sensitivity analysis approach to determine the range of optimality for the objective function coefficients.
Data from problem 12, chapter 2:
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 kilo of fuel additive is a mixture of 0.4 kilos of material 1 and 0.6 kilos of material 3. A kilo of solvent base is a mixture of 0.5 kilos of material 1, 0.2 kilos of material 2 and 0.3 kilos of material 3. After deducting relevant costs, the profit contribution is E40 for every kilo of fuel additive produced and E30 for every kilo of solvent base produced.
RMCâs 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 â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦.20 kilos
Material 2â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦... 5 kilos
Material 3â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦â¦ 21 kilos
Assuming that RMC is interested in maximizing the total profit contribution, answer the following:
Max 40F + 30S s.t + '/½s < 20 Material 1 /2s <5 Material 2 %SF+/10 S< 21 Material 3 2/F F,S20
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