Answer Happy

3. 1700 1800 1900 A car rental company currently has a surplus of 16 cars in location 1 and 18 cars in location 2. Other four locations of the company (Locations 3, 4, 5, and 6) need 10 cars each to support demand. The profit from getting cars from locations 1 and 2 to the other locations where they are sold are: Location Location Location Location Location 1 5400 2300 3000 Location 2 2400 3100 For example, the profit is $1700 if a car is shipped from location 1 to location 4 where it is sold. The linear programming model that solves this problem, where the variables are the number of cars shipped from location 'l' to location “I', is: Maximize Total profit Const 1: # of cars shipped to location 3 <=10 Const 2: # of cars shipped to location 4 <=10 Canet 2. # nf rare chinnad to Inpatinn 5c1n The Solver solution Variable Cells Final Value 10 0 6 Cell Name $D$10 From Location 1 To Location3 $E$10 From Location 1 To Location $F$10 From Location 1 To Locations $G$10 From Location 1 To Location 6 $D$11 From Location 2 To Location3 $E$11 From Location 2 To Location4 $F$11 From Location 2 To Locations $G$11 From Location 2 To Location Reduced Objective Cost Coefficient 0 5400 -500 1700 0 2300 -500 3000 -2600 2400 0 1800 0 1900 0 3100 Allowable Allowable Increase Decrease 1E+30 2600 500 1E+30 2600 500 500 1E+30 2600 1E+30 100 500 500 100 1E+30 500 0 0 4 4 10 OOO Constraints Final Value 10 4 Cell Name $D$12 Total To Location3 $E$12 Total To Location4 $F$12 Total To Location5 $G$12 Total To Location6 $H$10 From Location 1 Total $H$11 From Location 2 Total Shadow Price 3200 0 100 1300 2200 1800 Constraint R.H. Side 10 10 10 10 16 18 Allowable Allowable Increase Decrease 4 4 1E+30 6 4 4 4 6 4 4 6 4 10 10 16 18
G Answer the following questions: 3.1 What is the maximum total profit for this problem? Calculate and show your calculations. Use the Answers sheet. 3.2 Which location(s) does not receive all the cars needed? How many cars it falls short? a. Locations 3, 5, and 6, are missing 6 cars each b. Location 4, is missing 6 cars c. No location is missing any car 3.3 The profit per car shipped from location 'i' to location “f' was calculated by: Selling price at *j* minus transportation cost from 'l' to '). Management is expecting the transportation cost per car shipped from location 1 to location 4 decreases by $250. The operation manager wants to send one more car from location 1 to 4 because it becomes more profitable 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 profit cannot remain maximum if we do not take advantage of the shipping cost reduction. b. She is wrong, and no re-run is needed to answer this. The current shipping plan maximizes the profit, even after the profit increase 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. 3.4 Management anticipates demand in location 5 will decrease in the near future to 8 cars. What will happen to the total profit? 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 profit will remain the same. b. We must re-run. If the constraint changes, the optimal transportation plan must change, thus the profit will change too. To know the new total profit, we must re-run the model. c. No need to re-run. New Total profit = Old Total profit + (8)* (100). d. No need to re-run. New Total profit = Old Total profit - (2)*(100).