Overall since we have unused capacity and the dual

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-Overall, since we have unused capacity and the dual price is 0, we should not purchase additional frames. G) Suppose that there is flexibility to shift 15 hours of assembly time to test time. Will the same extreme point stay as the optimal solution? By how much does the optimal objective change? -Since the question is looking at shifting 15 hours of assembly time to test time, there are 2 constraints that limit this shift. The 2 constraints are x 3 (assembly time hours) and x 4 (test time hours). -First we look at output 1 to figure out whether or not this shift is in the range of these constraints. Since we are trying to decrease assembly time (x 3 ) from 1800 to 1785 AND the range for x 3 is between 1500 and 2033.333, this shift is in the range. Since we are trying to increase test time (x 4 ) from 500 to 515 AND the range for x 4 is between 360 and 560, this shift is in the range. Given that both of these changes are within the range, the same extreme point will remain as the optimal solution. -Furthermore, since there are two simultaneous changes in the right-hand side, the 100% rule for the range of feasibility will apply. The 100% rule states that simultaneous changes will not change the dual prices as long as the sum of the percentages of the changes divided by the corresponding maximum allowable change in the range of feasibility for each right-hand side does not exceed 100%. =Constraint 3: change/allowable decrease change + Constraint 4: change/allowable increase change = 15/300 + 15/60 = 0.3 x 100= 30% *Since the sum of the percentages of the changes does not exceed 100%, the dual prices are applicable. -To figure out how much the optimal objective changes due to this shift, we must look at the dual price for both of these constraints, x 3 and x 4 . The dual price is applicable because the change is within the range of both of these constraints and the sum of the percentages of the changes does not exceed 100%. It can be seen from output 1 that the dual price for both of these constraints is $5. This means that the decrease in assembly time hours results in a decrease of $75 ($5 x 15) and an increase in test time hours results in an increase of $75 ($5 x 15). Therefore, this shift is balanced so there is no change in the optimal objective value. H) Are there alternative optimal solutions? -When the value of x i in the optimal solution is 0 and the reduced cost associated with that x i is 0, this indicates that there are alternative optimal solutions. -In output 1, we can see that constraint 3 (x 3 ), the assembly time hours, has a value of 0 in the optimal solution and the reduced cost associated with x 3 is 0. This indicates that there are alternative optimal solutions.
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  • Spring '12
  • n/a
  • Operations Research, Limit of a function, $2, Management Scientist software, 66.667. -Therefore

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