Universal Products produces three types of industrial chemicals: products A, B, and C. The three chemicals...
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Universal Products produces three types of industrial chemicals: products A, B, and C. The three chemicals differ with respect to the amount of processing time required. During the manufacturing process, each product undergoes three different processes performed on three different machines. Processing time for each product type is shown in the following table, in terms of minutes per pound of product. The table also shows profit per pound for each product. 国 Product A 2.73 2.73 Product B Product C 3.74 Process 1 (minutes per pound) Process 2 (minutes per pound) Process 3 (minutes per pound) Profit per pound 3.21 4.42 1.82 1.87 0.91 1.59 $21 $26 $22 Over the next week there are 2000 minutes of processing time available for Process 1, 1900 minutes for Process 2, and 900 minutes for Process 3. Universal wants to maximize its profit while satisfying the constraints. The spreadsheet model of this LP is given on the sheet "Problem 3 Model" and the sensitivity report is given on sheet "Problem 3 Sensitivity Report", You can't (and don't need to) change the model or run Solver for this problem. Answer the following questions based on the information in the sensitivity report spreadsheet and write your answers on the spreadsheet "Problem 3 Answers" - (5 points) Suppose that the profit per pound for Product C was reduced to $20. Would the optimal values for the decision variables change? Why or why not? (5 points) Given the change to $20 profit per pound for Product C, would the optimal value of the objective function change? If so, can you tell what the new objective function value would be without running Solver again? If the value does change and can be determined, show your calculations and state what the new value would be. b. (5 points) Suppose that the prtofit per pound for Product A was increased to $3S (with all other profit per pound values at their original values). Would the optimal values for the MacBook Air a00 D00 F4 44 F7 F3 FS F8 $ & 4. 品 %# 3 be without running Solver again? If the value does change and can be determined, show your calculations and state what the new value would be. b. (5 points) Suppose that the profit per pound for Product A was increased to $35 (with all other profit per pound values at their original values). Would the optimal values for the decision variables change? Why or why not? (5 points) Given the change to $35 profit per pound for Product A, would the optimal value of the objective function change? If so, can you tell what the new objective function value would be without running Solver again? If the value does change and can be determined, show your calculations and state what the new value would be. e. (5 points) Suppose that minutes of processing time available for Process 1 has increased to 2500 (with all other values at their original values). What change will this cause in the optimal value of the objective function? Show calculations if the value can be calculated, or if it can't be calculated explain why. d. (5 points) Suppose that minutes of processing time available for Process I has decreased to 1950 (with all other values at their original values). What change will this cause in the optimal valuc of the objective function? Show your calculations if the value can be calculated, or if it can't be calculated explain why. e (5 points) What is the meaning of the shadow price value of 3.62 for the Process 2 Total Minutes constraint? Be specific in terms of this decision problem, clearly identifying which values will change, by how much they will change, and in what direction they will change, Also explain the range of values for the constraint's RHS over which the shadow price can be used. E (5 points) What would have to happen to the objective function coefficient for the Product B decision variable in order for Product B to be profitable to produce? Show your calculations. Be specific in terms of this decision problem, clearly identifying which value would have to change, by how much it would change, and in what direction it would change. 13 MacBook Air 20 F3 II 74 F7 F4 FS F6 #3 % & 3 4. 6. %24 Picture Charts fx A B D F H Production Planning Problem Inputs Product A B Process 1 Minutes Required for 1 Pound Process 2 Minutes Required for 1 Pound Process 3 Minutes Required for 1 Pound 2.73 3.21 3.74 2.73 4.42 1.87. 0.91 182 1:59 Profit per Pound $21.00 $26.00 $22.00 10 12 Production Plan A 13 Pounds Produced 659.34 0.00 53.48 14 15 16 17 Constraints RHS 2,000 1900 900 LHS 18 Process 1 Total Minutes Process 2 Total Minutes Process 3 Total Minutes 2,000.00 1,900.00 19 20 685.03 21 22 23 Objective alu 24 25 Total Prof15.022.62 28 29 Be 31 33 ge o4 35 37 = in or 40 pecific nge, b4 Problem 1 Problem 2 Problem 3 Model A Problem 3 Sensitivity Report Problem 3 Anew Ready W .. MacBook Air ome Insert Draw Page Layout Formulas Data Review Do you want to restart to updates now or try tonig Tables Data from Picture Add-ins Moco ed orChan lustrations AB Varable Cells Allowable Reduced Objective Cost Final Allowable Increase Decrease Coefficient 0.00 3.07 0.00 Name Value Cell $OS13 Pounds Produced A SES13 Pounds Produced B $F$13 Pounds Produced C 21 11.11764706 1.489812977 1E+30 659.34 0.00 26 3.07239819 53.48 22 4.748251748 7.615384615 D Constraints Allowable Allowable Shadow Price Final Constraint RH. Side Decrease Increase Value 2,000.00 1,900.00 Name Cell $DS18 Process 1 Total Minutes LHS 4.07 2000 415.862069 100 3 100 214.973262 900 SDS19 Process 2 Total Minutes LHS 1900 900 3.62 4 $D$20 Process 3 Total Minutes LHS 0.00 1E+30 685.03 6 17 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 Problem A Problem 3 Model A Problem Sensitivity Report Problem 1 Problem 2 Ready W Universal Products produces three types of industrial chemicals: products A, B, and C. The three chemicals differ with respect to the amount of processing time required. During the manufacturing process, each product undergoes three different processes performed on three different machines. Processing time for each product type is shown in the following table, in terms of minutes per pound of product. The table also shows profit per pound for each product. 国 Product A 2.73 2.73 Product B Product C 3.74 Process 1 (minutes per pound) Process 2 (minutes per pound) Process 3 (minutes per pound) Profit per pound 3.21 4.42 1.82 1.87 0.91 1.59 $21 $26 $22 Over the next week there are 2000 minutes of processing time available for Process 1, 1900 minutes for Process 2, and 900 minutes for Process 3. Universal wants to maximize its profit while satisfying the constraints. The spreadsheet model of this LP is given on the sheet "Problem 3 Model" and the sensitivity report is given on sheet "Problem 3 Sensitivity Report", You can't (and don't need to) change the model or run Solver for this problem. Answer the following questions based on the information in the sensitivity report spreadsheet and write your answers on the spreadsheet "Problem 3 Answers" - (5 points) Suppose that the profit per pound for Product C was reduced to $20. Would the optimal values for the decision variables change? Why or why not? (5 points) Given the change to $20 profit per pound for Product C, would the optimal value of the objective function change? If so, can you tell what the new objective function value would be without running Solver again? If the value does change and can be determined, show your calculations and state what the new value would be. b. (5 points) Suppose that the prtofit per pound for Product A was increased to $3S (with all other profit per pound values at their original values). Would the optimal values for the MacBook Air a00 D00 F4 44 F7 F3 FS F8 $ & 4. 品 %# 3 be without running Solver again? If the value does change and can be determined, show your calculations and state what the new value would be. b. (5 points) Suppose that the profit per pound for Product A was increased to $35 (with all other profit per pound values at their original values). Would the optimal values for the decision variables change? Why or why not? (5 points) Given the change to $35 profit per pound for Product A, would the optimal value of the objective function change? If so, can you tell what the new objective function value would be without running Solver again? If the value does change and can be determined, show your calculations and state what the new value would be. e. (5 points) Suppose that minutes of processing time available for Process 1 has increased to 2500 (with all other values at their original values). What change will this cause in the optimal value of the objective function? Show calculations if the value can be calculated, or if it can't be calculated explain why. d. (5 points) Suppose that minutes of processing time available for Process I has decreased to 1950 (with all other values at their original values). What change will this cause in the optimal valuc of the objective function? Show your calculations if the value can be calculated, or if it can't be calculated explain why. e (5 points) What is the meaning of the shadow price value of 3.62 for the Process 2 Total Minutes constraint? Be specific in terms of this decision problem, clearly identifying which values will change, by how much they will change, and in what direction they will change, Also explain the range of values for the constraint's RHS over which the shadow price can be used. E (5 points) What would have to happen to the objective function coefficient for the Product B decision variable in order for Product B to be profitable to produce? Show your calculations. Be specific in terms of this decision problem, clearly identifying which value would have to change, by how much it would change, and in what direction it would change. 13 MacBook Air 20 F3 II 74 F7 F4 FS F6 #3 % & 3 4. 6. %24 Picture Charts fx A B D F H Production Planning Problem Inputs Product A B Process 1 Minutes Required for 1 Pound Process 2 Minutes Required for 1 Pound Process 3 Minutes Required for 1 Pound 2.73 3.21 3.74 2.73 4.42 1.87. 0.91 182 1:59 Profit per Pound $21.00 $26.00 $22.00 10 12 Production Plan A 13 Pounds Produced 659.34 0.00 53.48 14 15 16 17 Constraints RHS 2,000 1900 900 LHS 18 Process 1 Total Minutes Process 2 Total Minutes Process 3 Total Minutes 2,000.00 1,900.00 19 20 685.03 21 22 23 Objective alu 24 25 Total Prof15.022.62 28 29 Be 31 33 ge o4 35 37 = in or 40 pecific nge, b4 Problem 1 Problem 2 Problem 3 Model A Problem 3 Sensitivity Report Problem 3 Anew Ready W .. MacBook Air ome Insert Draw Page Layout Formulas Data Review Do you want to restart to updates now or try tonig Tables Data from Picture Add-ins Moco ed orChan lustrations AB Varable Cells Allowable Reduced Objective Cost Final Allowable Increase Decrease Coefficient 0.00 3.07 0.00 Name Value Cell $OS13 Pounds Produced A SES13 Pounds Produced B $F$13 Pounds Produced C 21 11.11764706 1.489812977 1E+30 659.34 0.00 26 3.07239819 53.48 22 4.748251748 7.615384615 D Constraints Allowable Allowable Shadow Price Final Constraint RH. Side Decrease Increase Value 2,000.00 1,900.00 Name Cell $DS18 Process 1 Total Minutes LHS 4.07 2000 415.862069 100 3 100 214.973262 900 SDS19 Process 2 Total Minutes LHS 1900 900 3.62 4 $D$20 Process 3 Total Minutes LHS 0.00 1E+30 685.03 6 17 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 Problem A Problem 3 Model A Problem Sensitivity Report Problem 1 Problem 2 Ready W
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