Linear Programming

DUE: OCTOBER 16, 2014
CASE PROBLEM
The Southern Textile Mill produces 5 different fabrics. Each fabric can be woven on one or more of the mill’s 38 looms. The sales department’s forecast of demand for the next month is shown in Table 1 along with data on the selling price per yard, variable cost per yard, and purchase price per yard. The mill operates 24 hours a day and is scheduled for 30 days during the coming month.

Fabric

Demand
Selling Price
Variable Cost
Purchase Price
(yards)
$/yard
$/yard
$/yard
1
16,500
0.99
0.66
0.80
2
22,000
0.86
0.55
0.70
3
62,000
1.10
0.49
0.60
4
7,500
1.24
0.51
0.70
5
62,000
0.70
0.50
0.70
TABLE 1 – MONTHLY DEMAND, SELLING PRICE, VARIABLE COST, AND PURCHASE
PRICE DATA FOR SOUTHERN TEXTILE MILL FABRICS
The mill has 2 types of looms: dobbie and regular. The dobbie looms are more versatile and can be used for all 5 fabrics. The regular looms can produce only 3 of the fabrics. The mill has a total of 38 looms: 8 are dobbie and 30 are regular. The rate of production for each fabric on each type of loom is given in Table 2. The time required to change over from producing one fabric to another is negligible and does not have to be considered.

Loom Rate (yards/hour)
Fabric
Dobbie
Regular
1
4.63
--2
4.63
--3
5.23
5.23
4
5.23
5.23
5
4.17
4.17
TABLE 2 – LOOM PRODUCTION RATES FOR THE SOUTHERN TEXTILE MILL

The Southern Textile Mill satisfies all demand with either its own fabric or fabric purchased from another mill. Fabrics that cannot be woven at the Southern Mill because of limited loom capacity will be purchased from another mill. The purchase price of each fabric is also shown in
Table 1.

MANAGERIAL REPORT
I. -

Develop a Linear Programming Model that can be used to schedule production for the
Southern Textile Mill, and at the same time to determine how many yards of each fabric must be purchased from another mill. The model should be clear and complete.