Management Science
Introduction:
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’s forecast of demand for the next month is shown below, along with data on the selling price per yard, variable cost per yard and the purchase price per yard. The mill operates 24 hours a day and is scheduled to work 30 days during the coming month.
Monthly Demand, Selling Price, Variable Cost, and Purchase Price Data for the Scottsville Textile
Fabric Demand
(yards) Selling Price
($/yard) Variable Cost
($/yard) Purchase Price ($/yard)
1 16,500 0.99 0.66 0.80
2 22,000 0.86 0.55 0.70
3 62,000 1.10 0.49 0.60
4 7,500 1.24 0.51 0.70
5 62,000 0.70 0.50 0.70
The Mill has two types of looms: dobbie and regular. The dobbie looms are more versatile and can be used for all five fabrics. The regular looms can produce only three of the fabrics. The mill has a total of 38 looms: 8 are dobbie and 30 are regular. The rate of production of each fabric on each type of loom is given in the table below. The time required to change over from producing one fabric to another is negligible and does not have to be considered.
Fabric Dobbie Regular
1 4.63 -
2 4.63 -
3 5.23 5.23
4 5.23 5.23
5 4.17 4.17
Requirements:
Our project is to develop a linear programming model that can be used to answer the below questions:
1. The final production schedule and loom assignments for each fabric
2. The projected total contribution to profit
3. A discussion of the value of additional loom time (‘The Mill’ is considering purchasing a ninth doobie loom. What is your estimate of the monthly profit contribution of this additional loom?)
4. A discussion of the objective coefficient ranges
5. A discussion of how the objective of minimizing total costs would provide a different model than the objective of maximizing total profit contribution: How would the
The Scottsville Textile Mill produces five different fabrics. Each fabric can be woven on one or more of the mill’s 38 looms. The sales department’s forecast of demand for the next month is shown below, along with data on the selling price per yard, variable cost per yard and the purchase price per yard. The mill operates 24 hours a day and is scheduled to work 30 days during the coming month.
Monthly Demand, Selling Price, Variable Cost, and Purchase Price Data for the Scottsville Textile
Fabric Demand
(yards) Selling Price
($/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
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 of each fabric on each type of loom is given in the table below. The time required to change over from producing one fabric to another is negligible and does not have to be considered.
Fabric Dobbie Regular
1 4.63 -
2 4.63 -
3 5.23 5.23
4 5.23 5.23
5 4.17 4.17
Requirements:
Our project is to develop a linear programming model that can be used to answer the below questions:
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 doobie loom. What is your estimate of the monthly profit contribution of this additional loom?)
4. A discussion of the objective coefficient 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