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Question: The RMC Corporation blends three raw materials to produce two products: a fuel additive and a sol…

by | Nov 30, 2023 | Posted Questions



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 1/2 ton of material 1 and 1/2 ton of
material 3. A ton of solvent base is a mixture of 1/5 ton of
material 1, 3/5 ton of material 2, and 1/5 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 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.

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
1 13
2 9
3 13

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 a negative number, enter minus sign with it. If
necessary, enter the numbers as a common fraction.

Let
x1 = the number of
tons of fuel additive produced
x2 = the number of
tons of solvent base produced
d1+ = 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 additive produced is less than the
target of 20 tons
d2+ = 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 is less than the target
value of 15 tons

Min d1- + d2-
s.t.
x1 + x2 Material 1
x1 + x2 Material 2
x1 + x2 Material 3
x1 + x2 + d1+ + d1- = Goal 1
x1 + x2 + d2+ + d2- = Goal 2
x1,
x2, d1+, d1-, d2+, d2-
≥ 0

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