Problems

1. A firm has four factories, # 1, 2, 3, 4, which ship their output to two warehouses, A and B. The capacities of the factories for one month, the requirements of the warehouses for one month, and the costs of shipping one unit from each factory to each warehouse in dollars are given below.

1. Set up the transportation matrix.
2. What type of dummy constraint is required?
3. How many units are in the dummy constraint?
4. What is the objective function?
5. What are the constraints?

1. How do you enter the problem on the EXCEL spreadsheet?
2. How do you enter the objective function?
3. How do you enter the constraints?
4. What is the solution?
5. What is the total cost?
6. What is the interpretation of the 150 dummy units?

1. Set up the transportation matrix.
2. What type of dummy constraint is required?
3. How many units are in the dummy constraint?
4. What is the objective function?
5. What are the constraints?

4. Solve problem #3 by using an EXCEL spreadsheet.

1. How do you enter the problem on the EXCEL spreadsheet?
2. How do you enter the objective function?
3. How do you enter the constraints?
4. What is the solution?
5. What is the total cost?
6. What is the interpretation of the dummy units?

Solutions

1. a.

1. A dummy destination.
2. 150 units.
3. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image235::/sites/dl/free/0072443901/24520/Image235.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image235 (1.0K)</a>Image235
4. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image236::/sites/dl/free/0072443901/24520/Image236.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image236 (2.0K)</a>Image236

2. a. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image237::/sites/dl/free/0072443901/24520/Image237.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image237 (26.0K)</a>Image237
b. In cell D-10: =12*C3+10*D3+0*E3+14*C4+11*D4+0*E4+9*C5+12*D5+0*E5+8*C6+7*D6+0*E6.
c. In cell G-3: =C3+D3+E3
In cell G-4: =C4+D4+E4
In cell G-5: = C5+D5+E5
In cell G-6: = C6+D6+E6
In cell C-8: = C3+C4+C5+C6
In cell D-8: = D3+D4+D5+D6
In cell E-8: = E3+E4+E5+E6

Click on Tools; Click on Solver. Set target cell: D10; Min; by changing cells C3:E6.
Click on Add; Cell Reference C3:E6 >=; 0
Click on Add; Cell Reference F3; =; 250
Click on Add; Cell Reference F4: =; 400
Click on Add; Cell Reference F5; =; 450
Click on Add; Cell Reference F6; =, 350
Click on Add; Cell Reference C7, =, 600
Click on Add; Cell Reference D7, =, 700
Click on Add; Cell Reference E7, =, 150
Click on Solve; Highlight Answer Report
EXCEL cell D3 = matrix cell 1B = 250 units
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d,e. Here is the total cost of the optimum shipping schedule.

f. Origin #2 will produce 150 units less than it is capable of producing.

3. a.

4. a.

d,e. From - To Quantity Cost Product
1 D 200 $10 $ 2,000
1 - DUMMY 300 0 0
2 A 300 9 2,700
2 B 200 11 2,200
2 C 400 12 4,800
Total Cost $11,700

f. Factory #1 will have idle time.