Operations Research Assignment
1. The Ace Manufacturing Company has orders for three similar products:
_____________________________________
Orders
Product (units)
A 2000
B 500
C 1200
Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week, and the unit costs, are as follows:
Capacity
Machine (units)
1 1500
2 1500
3 1000
Product
Machine A B C
1 $1.00 $1.20 $0.90
2 $1.30 $1.40 $1.20
3 $1.10 $1.00 $1.20
Use the transportation model to develop the minimum-cost production schedule for the products and machines. Show the linear programming formulation.
2. Scott and Associates, Inc. is a consulting firm that has 4 new clients. Based on different background and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and estimated completion times in days are
Client
Project Leader 1 2 3 4
Jackson 10 16 32 10
Ellis 14 22 40 22
Smith 22 24 34 34
Burton 14 18 36 24
What is the optimal assignment?
3. Wilson Distributors, Inc. is opening two new sales territories in the western states. Three individuals currently selling in the Midwest and the East are being considered for promotion to regional sales manager positions in the new sales territories. Management has estimated total annual sales (in thousands of dollars) for the assignment of each individual to each sales territory. The management sales projections are as follows:
Sales Region
Regional Managers Northwest Southwest
Bostock $100 $95
McMahon $ 85 $80
Miller $ 90 $75
Formulate and solve a linear programming model to obtain the optimal solution.
4. Fowle Marketing Research has four project leaders available for
_____________________________________
Orders
Product (units)
A 2000
B 500
C 1200
Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week, and the unit costs, are as follows:
Capacity
Machine (units)
1 1500
2 1500
3 1000
Product
Machine A B C
1 $1.00 $1.20 $0.90
2 $1.30 $1.40 $1.20
3 $1.10 $1.00 $1.20
Use the transportation model to develop the minimum-cost production schedule for the products and machines. Show the linear programming formulation.
2. Scott and Associates, Inc. is a consulting firm that has 4 new clients. Based on different background and experiences of the leaders, the various leader-client assignments differ in terms of projected completion times. The possible assignments and estimated completion times in days are
Client
Project Leader 1 2 3 4
Jackson 10 16 32 10
Ellis 14 22 40 22
Smith 22 24 34 34
Burton 14 18 36 24
What is the optimal assignment?
3. Wilson Distributors, Inc. is opening two new sales territories in the western states. Three individuals currently selling in the Midwest and the East are being considered for promotion to regional sales manager positions in the new sales territories. Management has estimated total annual sales (in thousands of dollars) for the assignment of each individual to each sales territory. The management sales projections are as follows:
Sales Region
Regional Managers Northwest Southwest
Bostock $100 $95
McMahon $ 85 $80
Miller $ 90 $75
Formulate and solve a linear programming model to obtain the optimal solution.
4. Fowle Marketing Research has four project leaders available for