The Scottsville Textile Mill produces five different fabrics. Each fabric can be woven on one or more of the mill's 38 looms. The sales department has forecast demand for the next month. The demand data are shown in Table 1.0, 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.
The Mill has two types of looms: dobbie and regular. The dobbie looms are more versatile and can be used for all five fabrics. The regular looms can produce only three 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 1.1. The time to change over from producing one fabric to another is negligible and
does not have to be considered.
The Mill satisfies all demand with either its own fabric or fabric purchased from another mill. That is, fabrics that cannot be woven at The Mill because of limited loom capacity will be purchased from another mill. The purchase price of each fabric is also shown in Table 1.0.
Table 1.0
Monthly Demand, Selling Price, Variable Cost, and Purchase Price Data for The Mill
Demand:
|
Fabric
|
Demand (yards)
|
Selling Price ($/yard)
|
Variable Cost ($/yard)
|
Purchase Price ($/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 1.1
Loom Production Rates for The Mill Loom rate (yard/hour)
|
Fabric
|
Dibbie
|
Regular
|
|
1
|
4.63
|
--
|
|
2
|
4.63
|
---
|
|
3
|
5.23
|
5.23
|
|
4
|
5.23
|
5.23
|
|
5
|
4.17
|
4.17
|
* Fabrics 1 and 2 can be manufactured only on the dobbie loom.
Question
Develop a model that can be used to schedule production for The Mill, and at the same time, determine how many yards of each fabric must be purchased from another mill. Include a discussion and analysis of the following items in your answer:
1. The final production schedule and loom assignments for each fabric
2. The projected total contribution to profit
3. A discussion of the value of additional loom time (The Mill is considering purchasing a ninth dobbie loom. What is your estimate of the monthly profit contribution of this additional loom?)
4. A discussion of the objectives coefficients' ranges
5. A discussion of how the objective of minimizing total costs would provide a different model than the objective of maximizing total profit contribution. (How would the interpretation of the objective coefficients' rages differ for these two models?)