company currently has a surplus of 20 cars in location 1 and 25 cars in location 2. Other four locations of the company (Locations 3, 4, 5, and 6) need 10 cars each to support demand. The costs of getting cars from locations 1 and 2 to the other locations are: Location3 Location4 Locations Location 5400 1700 2300 Location 1 Location 2 3000 2400 1800 1900 3100 For example, it costs $1700 to ship a car from location 1 to location 4. The linear programming model that solves this problem, where the variables are the number of cars shipped from location 'I' to location “l', is: Minimize Total Transportation cost Const 1: # of cars shipped to location 3 =10 Const2: # of cars shipped to location 4 =10 Const 3: # of cars shipped to location 5=10 Const 4: # of cars shipped to location 6 =10 Const 5: # of cars shipped from location 1 ?? 20 Const 6: # of cars shipped from location 2 ?? 25
Variable Cells Reduced Allowable Allowable Final Value Objective Coefficient Cost 0 10 0 Cell $D$10 $E$10 $F$10 $G$10 $D$11 $E$11 $F$11 $G$11 Name From Location 1 To Location3 From Location 1 To Location From Location 1 To Locations From Location 1 To Location From Location 2 To Location3 From Location 2 To Location 4 From Location 2 To Locations From Location 2 To Location 6 10 5400 1700 2300 3000 2400 1800 1900 3100 Increase 1E+30 500 2600 500 2600 100 500 1E+30 Decrease 2600 1E+30 500 1E+30 1E+30 500 100 500 10 0 10 0 Constraints Constraint Allowable Allowable Shadow Final Value Decrease 4 10 10 Cell $D$12 $E$12 $F$12 $G$12 $H$10 SH$11 6 Name Total To Location Total To Location Total To Locations Total To Location From Location 1 Total From Location 2 Total Price 2400 1700 1900 3000 0 R.H. Side 10 10 10 10 20 Increase 4 1E+30 4 10 4 4 6 10 ?? ?? 4 4 0 25 6 4
3.1 What is the minimum total cost for this problem? Calculate and show your calculations. Use the Answers sheet. 3.2 Two signs in the linear model shown above are missing in the last two constraints. What are the signs missing? a. '<' in both constraints b. ' in both constraints C. '=' in both constraints d. '>=' in both constraints 3.3 In the output shown, the shipment from Location 1 and Location 2 are missing. Enter these shipments in the Answers sheet. a. Impossible to answer. We need to Rerun b. 10 from each location c. 20 from each location d. Any shipments that amount to 40 cars is optimal
3.4 Management is expecting the transportation cost per car shipped from location 1 to location 4 decrease by $250. The operation manager wants to send one more car from location 1 to 4 because it becomes less expensive by $250. Is she right? Choose the correct answer: a. She is right, and she does not need to re-run the model to know this. Total cost will be minimized if we send one more car on this route taking vantage of the shipping cost reduction. b. She is wrong, and no re-run is needed to answer this. The current shipping plan minimizes the total cost, even after the cost deccrease per car on this route is included. C. She may be right or wrong, but we can only know this after we re-run the model. 3.5 Management anticipates demand in location 5 will decrease in the near future to 8 cars. What will happen to the total transportation cost? Do you need to rerun in order to answer? a. No need to rerun. The optimal solution will not change because the change in demand is within the allowable decrease. Thus, the total cost will remain the same. b. We must re-run. If the constraint changes, the optimal transportation plan must change, thus the cost will change too. To know the new total cost, we must re- run the model. C. No need to re-run. New Total cost = Old Total cost + (2)*(1900) d. None of the above
3. A car rental 3. A car rental company currently has a surplus of 20 cars in location 1 and 25 cars in location 2. Other four locations
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