Homework 2 solution

Homework 2 solution - Problem 3.10b Coffee Country Roasters...

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Problem 3.10b Coffee Country Roasters Tons Grade A available 0.5 0.2 100 Grade B available 0.2 0.5 100 Grade C available 0.3 0.3 75 Profit per ton 150 120 Tons to produce: 166.6667 83.33333 LHS sign RHS Grade A available 100 < 100 Grade B available 75 < 100 Grade C available 75 < 75 Total Profit: 35000 Sensitivity Report Best Blend Economy Blend Part a. Let B be the tons of Best Blend produced. Let E be the tons of Economy Blend produced. MAX: Profit = 150B + 120E subject to: 0.5B + 0.2E < 100 Grade A available 0.2B + 0.5E < 100 Grade B available 0.3B + 0.3E < 75 Grade C available B, E > 0 Non-negativity c. Since a decreased profit of 10 is within the allowable decrease, the production plan will not change. The profit will change by (-$10/ton)(83.333 tons). The profit will go down by $833.33. d. A decrease of 20 tons is within the allowable decease so the shadow price is valid for this change. Since the shadow price is 0 for this constraint, it is not a binding constraint and there is no impact on the optimal production plan and total profit. e. An increase of 12 tons of Grade C is beyond the allowable increase so the shadow price is not valid. The first 10.71 tons of Grade C beans are worth $333.33 per ton ($3,570.) If we assume that any beans beyond the allowable increase have a value greater than or equal to 0, the 12 tons of Grade C beans would be worth at least $3,570. You should take the deal because your profit will go up at least $570. The production plan and profit will be affected. Variable Cells Final Reduced Objective Allowable Allowable Cell Name Value Cost Coefficient Increase Decrease $B$9 Tons to produce: Best Blend 166.6666667 0 150 150 30 $C$9 Tons to produce: Economy Blend 83.33333333 0 120 30 60 Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$12 Grade A available LHS 100 100 100 25 25 $B$13 Grade B available LHS 75 0 100 1E+30 25 $B$14 Grade C available LHS 75 333.3333333 75 10.71428571 15
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Microsoft Excel 14.0 Answer Report Worksheet: [Chapter_3_Linear_Models_Solution.xlsx]3.10 Report Created: 9/13/2011 10:56:34 AM Result: Solver found a solution. All Constraints and optimality conditions are satisfied. Solver Engine Engine: Simplex LP Solution Time: 0.078 Seconds. Iterations: 2 Subproblems: 0 Solver Options Max Time Unlimited, Iterations Unlimited, Precision 0.000001, Use Automatic Scaling Max Subproblems Unlimited, Max Integer Sols Unlimited, Integer Tolerance 1%, Assume NonNegative Objective Cell (Max) Cell Name Original Value Final Value $B$16 Total Profit: LHS 390 35000 Variable Cells Cell Name Original Value Final Value Integer $B$9 Tons to produce: Best Blend 1 166.6666666667 Contin $C$9 Tons to produce: Economy Blend 2 83.3333333333 Contin Constraints Cell Name Cell Value Formula Status Slack $B$12 Grade A available LHS 100 $B$12<=$D$12 Binding 0 $B$13 Grade B available LHS 75 $B$13<=$D$13 Not Binding 25 $B$14 Grade C available LHS 75 $B$14<=$D$14 Binding 0
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Microsoft Excel 14.0 Sensitivity Report
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This note was uploaded on 01/17/2012 for the course MGMT 306 taught by Professor Staff during the Spring '08 term at Purdue University.

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Homework 2 solution - Problem 3.10b Coffee Country Roasters...

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