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to ME30B main pageDeviation from the Goal
By doing the graphical method or using Lindo to the problem found in Page 1, you would have found that the solution to the problem is
L = 4 and E = 0. This means 400 gallons of latex paint is produced and 0 gallons of enamel paint
Lets look back at each of our goals.
Goal 1 (Overtime Labour)
10 L + 15 E ≤ 40
10 L + 15 E + Y1- – Y1+ = 40
Thus if we evaluate our goal we have
10(4) + 15 (0) = 40 hours
Therefore, our goal has been met exactly. We have not used any overtime labour. There is no deviation from our goal, i.e. Y1- = Y1+= 0
Inserting these values we have:
10(4) + 15 (0) + 0 + 0 = 40 hours
Goal 2 (Profit)
100 L + 100 E ≥ 1000
100 L + 100 E + Y2- – Y2+ = 1000
Evaluating our goal
100(4) + 100(0) = 400
Our goal is a $1000, but we have only achieved $400. Thus, we have fallen short of our goal, by $600 (i.e. $1000 - $400 = $600). Since, we have not exceeded our goal, then Y2+ = 0. The corresponding variable for fallen short of our goal is our slack deviation variable, and thus Y2- = $600.
Therefore inserting these values we have:
100 (4) + 100 (0) + 600 – 0 = 1000
Goal 3 (Enamel Paint Production)
E ≥ 7
E + Y3- – Y3+ = 7
Thus if we evaluate our goal:
Goal 3 = 0
Therefore our goal is 700 gallons of enamel paint, however we are producing 0 gallons of enamel paint. This means we have fallen short of our goal by 700 (i.e. 700 - 0 = 700 enamel paint). We have not exceeded our goal, therefore, Y3+ = 0. We have however, fallen short of goal, which corresponds to the slack variable, Y3- = 7. Remember that the deviation variables are measured in 100 gallons of paint.
Therefore inserting these values we have
0 + 7 – 0 = 7
Here is some additional information:
Objective function
If we look back at our objective function
Min P1Y1+ + P2Y2- + P3Y3-
Let us insert the values we found for the deviation variables
P1(0) + P2(600) + P3(7) = 600 P2 + 7 P3
This equation summarizes the extent to which the goals were met.
Constraints
Let us take a look at our constraints
Constraint 1 (Labour)
10 L + 15 E ≤ 70
Substituting the values
10 (4) + 15 (0) = 40
Therefore the constraint is non-binding and there is a slack of 70 – 40 = 30 hrs. The 30 hrs corresponds the overtime which we did not use (as found in Goal 1).
Constraint 2 (Production Constraint)
L – E ≥ 0
Substituting E and L values
4 – 0 = 4
Therefore this constraint is non-binding and there is an excess of 400 gallons of paint (i.e. 4 – 0 = 4 100-gallons of paint ).
Note: Remember the minimum required was for E and L to be equal or in other words L – E = 0