Use the sensitivity reports to answer the following questions: Your objective is

Question

Use the sensitivity reports to answer the following questions: Your objective is to Max total profit ($). What is the value of the optimal Z*? Which constraint(s) are not binding? Independently consider the following options, which one(s) would you consider pursuing, if any? [Circle Y or N for each row] Buy 10 extra units of Raw material for a total of $500 Y N Sell 2 m^3 of Storage 1 for a total of $80 Y N Buy 3 m^3 of Storage 2 for a total of $3 Y N Hire 5 more workers for $15 each Y N The first OF coefficient c_1 = 90. What would happen to Z*, xl*, x2*?

Explanation / Answer

a.

The optimal total profit Z* = (120 x 6) + (170 x 2) = 720 + 340 = $1060

b.

The non binding constraints are those whose value does not attain its right hand side value.

So the constraint of workers used and storage 2 are not binding.

c.

Buying 10 extra units of Raw material for a total of $500 will increase the profit by (10 x 42.5) = $425 as the shadow price for this constraint is 42.5 and the allowable increase is 12. So the change in profit will be 425 - 500 = -75. So option N can be chosen.

Selling 2m3 of Storage 1 for a total of $80 will decrease the profit by (2 x 35) = $70 as the shadow price for this constraint is 35 and the allowable decrease is 6. So the change in profit will be (80 - 70) = 10. So option Y can be chosen.

Buying 3m3 of Storage 2 for a total of $3 will not change the profit as this constraint is not binding and the shadow price is zero. So the change in net profit will be -3. So option N can be chosen.

Hiring 5 more workers for $15 each will not change the profit as this constraint is not binding and the shadow price is zero. It will reduce the profit by 75 for extra expenses only. So option N can be chosen.

d.

Changing the objective coefficient c1 from 120 to 90 will not affect the optimal values. It will only change the value of the profit but it will be the optimal. This is because the allowable decrease for c1 is 35. So changing it from 120 to 90 will not change x1* and x2* but will change Z*.

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