LINEAR PROORAMMING 101 5.9. Paint it Easy The president of the \"Paint it Easy\"
ID: 3043801 • Letter: L
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LINEAR PROORAMMING 101 5.9. Paint it Easy The president of the "Paint it Easy" paint company is in trouble: People complain that the paint does not last long. Experts now recommend a new formula such that Boiling point 70°C Hardening point4 hr Plastic ss 70% by volume Acid 15% by volume Four components, A-D, can be used to produce the paint. Their contribution to each of the preceding characteristics is in proportion to their part in the mixture The coefficients are: 15 Boiling point Hardening time (h) % plastic %acid Price per liter (S) 60 30 50 0 80 0 0.8 Write the paint production problem as a cost minimization and explain the decision variables, objective function, and contraints.Explanation / Answer
Let us define the following variable, which are called as decision variables:
U : Proportion of component A in paint (in appropriate units)
V : Proportion of component B in paint (in appropriate units)
W : Proportion of component C in paint (in appropriate units)
W : Proportion of component D in paint (in appropriate units)
Then total price is computed as Z = 1.0U+2.4V+1.5W+0.8X
Our objective is to minimize this price, i.e.
Minimize Z = 1.0U+2.4V+1.5W+0.8X
There will be four conditions for each parameter, which are as follows:
Condition on Boiling Point:
60U+99V+15W+30X 70
Condition on Hardening Time:
1U+4V+3W+2X 4
Condition on % Plastic:
80U+50V+2W+14X 70%(U+V+W+X)
i.e. 80U+50V+2W+14X 0.70(U+V+W+X)
i.e. 79.3U+49.3V+1.3W+13.3X 0
Condition on % Acid:
20U+10X 15%(U+V+W+X)
i.e. 20U+10X 0.15(U+V+W+X)
i.e. 19.85U-0.15V-0.15W+9.85X 0
Finally Linear Programming Problem can be set as follows:
Minimize Z = 1.0U+2.4V+1.5W+0.8X
Subject to the constraints,
60U+99V+15W+30X 70
1U+4V+3W+2X 4
79.3U+49.3V+1.3W+13.3X 0
19.85U-0.15V-0.15W+9.85X 0
And non-negativity restrictions U 0, V 0, W 0, X 0
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