In the attached file containing the sensitivity report for the Bolvill Mukluk Fa
ID: 3239329 • Letter: I
Question
In the attached file containing the sensitivity report for the Bolvill Mukluk Factory problem BMsensitivityreport.1.pdf explain what the shadow price and the allowable increase and decrease means for sewing.
Variable Cells Final Reduced Objective Allowable Allowable Name Cell Value Cost Coefficient Increase Decrease 30 SBS18 Changing Cells (number of each decision variable) x1 10 1E+30 SC$18 Changing Cells (number of each decision variable) x2 80 1E+30 20 Constraints Final Shadow Constraint able Allowable Cell Name Value Price R.H. Side Increase Decrease SBS18 Changing Cells (number of each decision variable) x1 1E+30 $C$18 Changing Cells (number of each decision variable) X2 3 1E+30 cutting Formula for each constraint 12 1E+30 12 sewing Formula for each constraint 20 16 12 Market Formula for each constraint 10Explanation / Answer
The “Shadow Price” value in the table can defined as the marginal value of one additionalunit in the right hand side value of a constraint, also known as dual values. For example,the shadow price of a packing constraint is $6.65, which means for every additional hourof packing, the total profit will increased by $6.65. The shadow price is still valid onlywhen the change in the right hand side value is within the “Allowable Increase” and“Allowable Decrease” value. For instance, the allowable increase and decrease for apacking constraint is 90, which means the maximum right hand side value can increasedto 540 (= 450 + 90) and minimum can decreased to 330 (= 450 – 90). Within that range,the shadow price is valid, but if the value of right hand side increased or decreasedbeyond the range, the shadow price will no longer valid. If the right hand side valueincreased to the maximum, the total profit can also increase by $594. For a nonbindingconstraint, the shadow price will be zero
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