Question

Can you please help me solve this problem? Thank you!

You have worked the Carolina Mobile Home transportation problem. Suppose there is a down turn in business and the sales lots must reduce sales by one mobile home per month to all locations except Charlotte. That is, Richmond will need 7 Greensboro will need 3 and Columbia will need 8 per month. What is the new Z value (shipping cost per month)? Is this a max or min problem? min Which manufacturing site or sites will need to reduce production?-- Is the model in balance with this reduction? no decimals for any answers) (Wilmington, Roanoke, or New Bern) (yes or no) You have graduated from NC A&T and joined Carolina Mobile Homes (CMH). CMH builds in three cities and ships to four cities. You have been requested to use your supply chain skills to reduce the shipping costs CMH has 3 factories in the cities of Roanoke Rapids, NC, Wilmington, NÇ and New Bern, NC. The factories produce 8 nits in Wilmington per month, Roanoke Rapids 10 units per month, and New Bern 9 units per month. The shipments arrive at the lots in the four cities of Richmond, Greensboro, Charlotte and Columbia in the follow quantities: Richmond 8, Greensboro 4, Charlotte 6 and Columbia 9. dtan 1049 The price to ship a mobile home is in the table below. 3 Table 1: Shipping Cost between Cities 1L7 Cost per Mobile Home Transported Into-> From Richmond Greensboro Charlotte Columbia Wilmingtorn Roanoke Rapids 1049 329 904 830 790 916 1118 826 1181 1172 New Bem 757 Presently all the units built at Wilmington ship to Richmond. All of the units produced at New Bern go to Columbia, South Carolina. The units produced at Roanoke Rapids ship to Greensboro and Charlotte. Under the current plan, what is the cost per month to Draw the network. Is this network balanced? Is this a max or min problem? Write the objective function How many variables do you have? How many constraints are there? List the constraint out of Wilmington? ship from the factories to the sales lot sites?

Answer 1

The current cost is 26656

	Richmond	Greensboro	Charlotte	Columbia	Supply
Wilmington	1049	830	790	826	8
Roanoke Rapids	329	555	916	1181	10
new Bern	904	757	1118	1172	9
Demand	8	4	6	9
Allocation	Richmond	Greensboro	Charlotte	Columbia
Wilmington	8
Roanoke Rapids		4	6
New Bern				9
Total cost	26656

The network is balanced. This is because Supply = Demand

This is a minimization problem

Let the factories be i ={1,2,3} and destinations be j={1,2,3,4} and the let Xij denote the quantity. The Cost between i and j be Cij. Then the objective function is

Minimize ∑ Xij*Cij

We have total of 3*4 = 12 decision variables

We have total of 7 constraints

Constraint out of Wilmington is

∑ X1j <= 8

The optimal solution is shown below

	Richmond	Greensboro	Charlotte	Columbia	Supply
Wilmington	1049	830	790	826	8
Roanoke Rapids	329	555	916	1181	10
new Bern	904	757	1118	1172	9
Demand	8	4	6	9
Allocation	Richmond	Greensboro	Charlotte	Columbia
Wilmington	0	0	0	8	8
Roanoke Rapids	8	0	2	0	10
New Bern	0	4	4	1	9
	8	4	6	9
Total cost	19744

If the demands the modified then the optimal solution is shown below

	Richmond	Greensboro	Charlotte	Columbia	Supply
Wilmington	1049	830	790	826	8
Roanoke Rapids	329	555	916	1181	10
new Bern	904	757	1118	1172	9
Demand	7	3	6	8
Allocation	Richmond	Greensboro	Charlotte	Columbia
Wilmington	0	0	0	8	8
Roanoke Rapids	7	0	3	0	10
New Bern	0	3	3	0	6
	7	3	6	8
Total cost	17284

The new Z value is 17284

This is a minimization problem

The model is not a balanced problem anymore because the supply does not equal demand.