Decision Science Problem 14-01 The RMC Corporation blends three raw materials to

Question

Decision Science

Problem 14-01 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 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. 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 materia material 1, 20 tons; material 2,5 tons; material 3, 21 tons. Management wants to achieve the following P1 priority level goals: Goal 1: Produce at least 30 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

Explanation / Answer

We can simply calculate whether it is possible for management to achieve P1 level goals or not, by taking,

Fuel additive =30 tons and solvent base = 15 tons and putting this values in the raw material formulas as given below:

Raw material       amount needed to achieve both P1 goals

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1                              2/5*(Fuel additive) + ½*(solvent base    )

2                              1/5*(solvent base)

3                              3/5*(Fuel additive) + 2/10*(solvent base)

Now taking

Fuel additive =30 tons and solvent base = 15 tons

Raw material       amount needed to achieve both P1 goals

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1                              2/ 5 (30) + 1/ 2 (15) = 12 +7.5 = 19.5

2                              1/ 5 (15) = 3

3                              3/ 5 (30) + 3/ 10 (15) = 18 + 4.5 = 22.5

Here it shows , we require 22.5 tons of material 3 to achieve this goal.

Since there are only 21 tons of Material 3 available, it is not possible to achieve both goals.

So answer is, this is not possible.

b)

X 1 = No of tons of fuel

X 2 = No of tons of solvent

Z = Objective equation

Z = 30 X1 + 15 X2

2/5 X1 + ½ X2 <= 20 Material 1

1/5 x2 <= 5 Material 2
3/5 x1 + 3/10 x2 <= 21 Material 3
x1 = > 0
x2= > 0

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