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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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