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94 CHAPTER 3 LINEAR PROGRAMMING: SENSITIVITY ANALYSIS AND INTERPRETATION OF SOLUTION

Figure 3.3 Effect of a Ten-Unit Change in the Right-Hand Side of the Cutting And
Dyeing Constraint

D
800
Objective Function Line

600 C & D 10S + 9D = 7711.75 New Feasible Region
Number of Deluxe Bags 400 I & P ( S = 527.50 )
Includes This Shaded Area
Optimal
Solution
D = 270.75

200 0.7S + D = 640

F
0 200 400 600 800 S
Number of Standard Bags

That is, allowing a marginal (one unit) change in the constraint. We can now solve
Equations. 3.7 and 3.6 to find the new optimal solution which is:

S ¼ 538:75
D ¼ 253:875
Profit contribution ¼ $7672:375
Confirming that if we increase the cutting and dyeing constraint by one hour then
profit contribution increases by $4.375. However, we can now undertake the same
analysis on the other constraints, again seeing how a marginal increase in the right-
hand side of a constraint changes the value of the objective function. If we look at a
marginal change in the finishing constraint we have:
0:7S þ 1D ¼ 630

1S þ 0:6667D ¼ 709
which gives a new solution of:
S ¼ 541:875
D ¼ 250:6875

Profit contribution ¼ 7674:9375
In the case of the finishing constraint, there is an increase in profit contribution of
$6.9375 for a marginal increase in finishing hours. But what about the other two

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