GasGo Chemical Company GCC blends three raw materials to pro

GasGo Chemical Company (GCC) blends three raw materials to produce its two primary products: a fuel additive and a solvent base.

A ton of fuel aditive contains .4 tons of material 1 and .6 tons of material 3

A ton of solvent base contains .5 tons of material 1, .2 tons of material 2, and .3 tons of material 3

For the current production period, GCC has these limited amounts of raw materials at its main plant: material 1, 20 tons; material 2, 5 tons; material 3, 21 tons. Additional amounts of material 3 might be obtained if necessary from another GCC plant.

Management has agreed to three goals:

Priority 1 Goals:

1. Produce at least 30 tons of fuel additive

2. Produce at least 15 tons of solvent base

Priority 2 Goal

3. Use no more than the 21 tons of material 3 available at the main plant.

Questions:

Develop a Goal Programming Model (with 2 non-goal constraints and 3 goals). In your model, define these decision variables X1 - tons of fuel additive produced, X2, tons of solvent base produced.

Explain in full how you would solve the model using priority sequencing. Then explain in full how you would solve again using order-of-magnitude weights.

What variable\'s solution value will answer the question, \"How many tons of material 3 should be obtained from GCC\'s other plant?\"

Solution

Raw Materials I II III Fuel aditive x 0.4 0 0.6 Solvent base y 0.5 0.2 0.3 Total 0.4x+0.5y 0.2y 0.6x+0.3y Available 20 5 21 Ext sources NO No yes x>=30 y>=15 0.6x+0.3y<=21 i.e. 2x+y<=70 Since \"Use no more than the 21 tons ..\" is given outside purchase = Nil 0.4x+0.5y<=20 i.e. 4x+5y<=200 0.2y<5 y<=25 2x+y<=70 If x=30, y =15 then 4x+5y=195<=200                                       2x+y=75>=70 Hence 5 units of C must be purchased from outside. So for priority 1 goal 5 tons of material 3 must be purchased from outside.