Homework answers / question archive / Course Number & Title: MGT4310  Operations Management HOMEWORK 3 Lauren Moore has sold her business for $500,000 and wants to invest in condominium units (which she intends to rent) and land (which she will lease to a farmer)

Course Number & Title: MGT4310  Operations Management HOMEWORK 3 Lauren Moore has sold her business for $500,000 and wants to invest in condominium units (which she intends to rent) and land (which she will lease to a farmer)

Operations Management

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Course Number & Title: MGT4310  Operations Management

HOMEWORK 3

1. Lauren Moore has sold her business for $500,000 and wants to invest in condominium units (which she intends to rent) and land (which she will lease to a farmer). She estimates that she will receive an annual return of $8,000 for each condominium and $6,000 for each acre of land. A condominium unit costs $70,000, and land costs $30,000 per acre. A condominium will cost her $1,000 per unit, an acre of land will cost $2,000 for maintenance and upkeep, and $14,000 has been budgeted for these annual expenses. Lauren wants to know how much to invest in condominiums and land to maximize her annual return.
2. 1. Formulate a mixed integer programming model for this problem.
   2. Solve the problem by using excel solver

 

2. Mazy’s Department Store has decided to stay open for business on a 24-hour basis. The store manager has divided the 24-hour day into six 4-hour periods and has determined the following minimum personnel requirements for each period:

 

Time	Personnel Needed
Midnight ~ 4:00 a.m.	95
4:00 a.m. ~ 8:00 a.m.	220
8:00 a.m. ~ Noon	270
Noon ~ 4:00 p.m.	75
4:00 p.m. ~ 8:00 p.m.	310
8:00 p.m. ~ Midnight	130

 

Store personnel must report to work at the beginning of one of these time periods and must work for 8 consecutive hours. The store manager wants to know the minimum number of employees to assign to each 4-hour segment to minimize the total number of employees.

 

1. 1. Formulate a mixed integer programming model for this problem.    (b) Solve the problem by using excel solver

 

             

3. Globex Investment Capital Corporation owns six companies that have the following estimated        returns (in millions of dollars) if sold in one of the next 3 years:

 

 

Year Sold

(Estimated return, $1,000,000s)

Company	1	2	3
1	14	18	23
2	9	11	15
3	18	23	27
4	16	21	25
5	12	16	22
6	21	23	28

 

To operating funds, the company must sell at least $24 million worth of assets in year 1, $28 million in year 2, and $32 million in year 3. Globex wants to develop a plan for selling these companies during the next 3 years to maximize return. Formulate an integer programming model for this problem.

 

4. The Heartland Distribution Company is a food warehouse and distributor that has a contract with a grocery store chain in several Midwest and Southeast cities. The company wants to construct new warehouses/distribution centers in some of the cities it services to serve the stores in those cities plus all the other stores in the other cities that don’t have distribution centers. A distribution center can effectively service all stores within a 300-mile radius. The company also wants to limit its fixed annual costs to under $1,200,000. The company wants to build the minimum number of distribution centers possible. The following table shows the cities within 300 miles of every city and the projected fixed annual charge for a distribution center in each city.

 

City	Annual fixed charge ($1ks)	Cities within 300 miles
1. Atlanta	270	1, 2, 7
2. Charlotte	250	1, 2, 9
3. Cincinnati	410	3, 4, 5, 6, 7, 8
4. Cleveland	410	3, 4, 5, 8
5. Indianapolis	280	3, 4, 5, 6, 7, 10
6. Louisville	360	3, 5, 6, 7, 10
7. Nashville	290	1, 3, 5, 6, 7, 10
8. Pittsburgh	330	3, 4, 8, 9
9. Richmond	380	2, 8, 9
10. St. Louis	295	5, 6, 7, 10

Formulate an integer programming model for this problem.

5. Oranges are grown, picked and then stored in warehouses in Tampa, Miami, and Fresno.

Theses warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table shows the shipping costs per truckload (in hundreds of dollars), supply, and demand. Because of an agreement between distributors, shipments are prohibited from Miami to Chicago:

 

 

To

(

cost, in $

100)

 

From	New York	Philadelphia	Chicago	Boston	Supply
Tampa	9	14	12	17	150
Miami	11	10	6	10	250
Fresno	12	8	15	7	200
Demand	110	250	140	100

1. Draw a network of this problem.
2. Formulate an integer programming model for this problem.