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Operations Research Models and Methods
Problems Section
Problems for Linear Programming Models
- Product Mix Sensitivity Analysis


a. Bottlenecks for this situation:

The bottlenecks are the time on machine 1 and the market for product A.

b. Reduce the cost of raw material 1 from $6 per unit to $4 per unit:

The sensitivity analysis indicates that the objective for R1 can be reduced to: 6 - 2.28 and increased to 6 + 2.8. Since $4 falls within this range, we conclude that the solution does not change. The objective value will change.

c. Add 10 hours to the time available for machine 1:

The range for M1 indicates that we can increase the availability of the machine time to 150. In this range we keep the same basic solution. This means that the amount of C will change. Since A is at its upper bound and B at its lower, production of these products will not change. When we add 10 hours to machine time M1, the objective will increase by 1.65*10 = 16.5.

The profit before the change is

10*20 + 4*25 - 6*13.75 - 8*7.5 = 182.5

After the change the profit will be 182.5 + 16.5 = 199

d .Reduce by 10 hours the time available on machine 2:

Since that constraint is slack by 10 units, reducing the time availability by that amount will not affect any aspect of the solution, except the slack variable for the M2 constraint.

e. Revenue for product B that would justify producing this product:

If the revenue of B increases by 3.2 to 33.2 the solution would change. We assume that the solution will now produce B.


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Operations Research Models and Methods
by Paul A. Jensen
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