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The company wants to come up with an optimal shipping strategy that will allow it to minimize its total shipping cost. Sensitivity Report Adjustable Cells Cell $B$9 $C$9 $D$9 $B$10 $C$10 $D$10 $B$11 $C$11 $D$11 Constraints Cell $E$9 $E$10 $E$11 $B$12 $C$12 $D$12 Final Reduced Objective Allowable Allowable Name Value Cost Coefficient Increase Decrease X1 X2 X3 *48488 X4 X5 X6 X7 X8 X9 250 0 0 50 100 200 F1 F2 F3 R1 R2 R3 0 400 0 0 1 2 0 OO 250 350 400 300 500 200 0 0 1 0 3 Name Value Price Final Shadow Constraint NON34 -2 0 -2 1 3 2 3 2 4 2 2 2 3 1 1E+30 250 350 400 300 500 200 1E+30 1 1 2 1E+30 1 1E+30 Allowable R.H. Side Increase 50 0 100 0 0 0 Use the Sensitivity Report to answer the following questions: (A) Please formulate the linear programming model. 1E+30 1 2 1 1 1E+30 1 1E+30 3 Allowable Decrease 0 1E+30 0 50 100 200 (B) Will any of the retail outlets experience any shortages in meeting their demand re- quirements if we implement the optimal solution? (C) Will any of the factories have any remaining quantities of the product if we imple- ment the optimal solution? (D) What is the total minimal shipping cost?

The company wants to come up with an optimal shipping strategy that will allow it to minimize its total shipping cost. Sensitivity Report Adjustable Cells Cell $B$9 $C$9 $D$9 $B$10 $C$10 $D$10 $B$11 $C$11 $D$11 Constraints Cell $E$9 $E$10 $E$11 $B$12 $C$12 $D$12 Final Reduced Objective Allowable Allowable Name Value Cost Coefficient Increase Decrease X1 X2 X3 *48488 X4 X5 X6 X7 X8 X9 250 0 0 50 100 200 F1 F2 F3 R1 R2 R3 0 400 0 0 1 2 0 OO 250 350 400 300 500 200 0 0 1 0 3 Name Value Price Final Shadow Constraint NON34 -2 0 -2 1 3 2 3 2 4 2 2 2 3 1 1E+30 250 350 400 300 500 200 1E+30 1 1 2 1E+30 1 1E+30 Allowable R.H. Side Increase 50 0 100 0 0 0 Use the Sensitivity Report to answer the following questions: (A) Please formulate the linear programming model. 1E+30 1 2 1 1 1E+30 1 1E+30 3 Allowable Decrease 0 1E+30 0 50 100 200 (B) Will any of the retail outlets experience any shortages in meeting their demand re- quirements if we implement the optimal solution? (C) Will any of the factories have any remaining quantities of the product if we imple- ment the optimal solution? (D) What is the total minimal shipping cost?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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The company wants to come up with an optimal shipping strategy that will allow it to minimize its total shipping cost. Sensitivity Report Adjustable Cells Cell $B$9 $C$9 $D$9 $B$10 $C$10 $D$10 $B$11 $C$11 $D$11 Constraints Cell $E$9 $E$10 $E$11 $B$12 $C$12 $D$12 Final Reduced Objective Allowable Allowable Coefficient Increase Decrease Name Value Cost X1 250 X2 0 X3 0 X4 50 X5 100 X6 200 X7 0 X8 400 X9 0 F1 F2 F3 R1 R2 R3 0 1 2 0 0 Final Shadow Name Value Price 250 350 400 300 500 200 0103 -2 0 -2 3 4 2 1 3 2 3 4 2 2 2 3 1 1E+30 1E+30 1 1 2 1E+30 1 1E+30 Constraint Allowable R.H. Side Increase 250 350 400 300 500 200 50 0 100 0 0 0 1E+30 1 2 1 1 1E+30 1 1E+30 3 Allowable Decrease 0 1E+30 0 50 100 200 Use the Sensitivity Report to answer the following questions: (A) Please formulate the linear programming model. (B) Will any of the retail outlets experience any shortages in meeting their demand re- quirements if we implement the optimal solution? (C) Will any of the factories have any remaining quantities of the product if we imple- ment the optimal solution? (D) What is the total minimal shipping cost? (E) Suppose that the shipping cost per unit for variable X₁ (i.e., route F1-R1) increases to $2.00. What impact will this have on the current optimal solution and the objective function value? (F) Suppose that the shipping cost per unit for variable X6 (i.e., route F2-R3) increases by $2.00 to $5.00. What impact will this have on the current optimal solution and the objective function value? (G) Suppose that the factory constraints and the retail outlet constraints become "<". What would the optimal solution and the objective function coefficient be? (Hint: The answer to this question is not given in the Sensitivity Report.)
Transcribed Image Text:The company wants to come up with an optimal shipping strategy that will allow it to minimize its total shipping cost. Sensitivity Report Adjustable Cells Cell $B$9 $C$9 $D$9 $B$10 $C$10 $D$10 $B$11 $C$11 $D$11 Constraints Cell $E$9 $E$10 $E$11 $B$12 $C$12 $D$12 Final Reduced Objective Allowable Allowable Coefficient Increase Decrease Name Value Cost X1 250 X2 0 X3 0 X4 50 X5 100 X6 200 X7 0 X8 400 X9 0 F1 F2 F3 R1 R2 R3 0 1 2 0 0 Final Shadow Name Value Price 250 350 400 300 500 200 0103 -2 0 -2 3 4 2 1 3 2 3 4 2 2 2 3 1 1E+30 1E+30 1 1 2 1E+30 1 1E+30 Constraint Allowable R.H. Side Increase 250 350 400 300 500 200 50 0 100 0 0 0 1E+30 1 2 1 1 1E+30 1 1E+30 3 Allowable Decrease 0 1E+30 0 50 100 200 Use the Sensitivity Report to answer the following questions: (A) Please formulate the linear programming model. (B) Will any of the retail outlets experience any shortages in meeting their demand re- quirements if we implement the optimal solution? (C) Will any of the factories have any remaining quantities of the product if we imple- ment the optimal solution? (D) What is the total minimal shipping cost? (E) Suppose that the shipping cost per unit for variable X₁ (i.e., route F1-R1) increases to $2.00. What impact will this have on the current optimal solution and the objective function value? (F) Suppose that the shipping cost per unit for variable X6 (i.e., route F2-R3) increases by $2.00 to $5.00. What impact will this have on the current optimal solution and the objective function value? (G) Suppose that the factory constraints and the retail outlet constraints become "<". What would the optimal solution and the objective function coefficient be? (Hint: The answer to this question is not given in the Sensitivity Report.)
E Modeling and Analysis 1. A company can ship its product from any of its three factories, F1, F2, and F3, to any of its retail outlets, R1, R2, and R3. The capacity, demand, and shipping cost information is provided as follows: Demand and Capacity Demand (units) R1: 300 R2: 500 R3: 200 Capacity (units) F1: 250 F2: 350 F3: 400 Shipping Cost/unit ($) R1 R2 R3 F1 1 3 F2 3 4 F3 2 2 2 2 3
Transcribed Image Text:E Modeling and Analysis 1. A company can ship its product from any of its three factories, F1, F2, and F3, to any of its retail outlets, R1, R2, and R3. The capacity, demand, and shipping cost information is provided as follows: Demand and Capacity Demand (units) R1: 300 R2: 500 R3: 200 Capacity (units) F1: 250 F2: 350 F3: 400 Shipping Cost/unit ($) R1 R2 R3 F1 1 3 F2 3 4 F3 2 2 2 2 3
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