management project
HW-6
Problem 2 (11 points)
The distribution system for the Herman Company consists of three plants, two warehouses, and four customers. Plant capacities and shipping costs per unit (in $) from each plant to each warehouse are as follows.
Plant
Warehouse
Capacity
1
2
1
4
7
450
2
8
5
600
3
5
6
380
Customer demand and shipping costs per unit (in $) from each warehouse to each customer are as follows.
Formulate a linear programming model of the problem. (Let Plant 1 be node 1, Plant 2 be node 2, Plant 3 be node 3, Warehouse 1 be node 4, Warehouse 2 be node 5, Customer 1 be node 6, Customer 2 be node 7, Customer 3 be node 8, and Customer 4 be node 9.
Warehouse
Customer
1
2
3
4
1
6
4
8
4
2
3
6
7
7
Demand
300
300
300
400
a) Define the decision variables. (1 point)
b) Define the objective function (2 points)
c) Define the constraints (5 points)
d) Determine an optimal solution (3 points)
Part-2 (9 points)
Please answer plan 2 of Example 3 (Slide #16) in CH-5-Part-3PowerPoint. ABC company uses the lease contract to replace equipment at least every two years.
The initial lease payment is $60,000. After that, the equipment price increases by 2% every year, and the trade-in credit for equipment used for one year is 30% of the equipment price and 10% for two years of use. ABC company wants to minimize the leasing costs over the next five years when replacing onesequipment under plan 2.
a) Define the decision variables (1 point)
b) Define the objective function (3 points)
c) Define the constraints (3 points)
d) Determine an optimal solution using Solver. ( 2 points)
Requirements: Listed