Management Science

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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 FabricDemand
(yards)Selling Price
($/yard)Variable Cost
($/yard)Purchase Price ($/yard)
116,5000.990.660.80
222,0000.860.550.70
362,0001.100.490.60
47,5001.240.510.70
562,0000.700.500.70

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 DobbieRegular
14.63-
24.63-
35.235.23
45.235.23
54.174.17

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 interpretation of the objective coefficients ranges differ for these two models?

Methods used to create Linear Program:
Objective:
To maximize Profit
Decision Variables:
Qty of Fabric 1 made on Dobbie
Qty of Fabric 2 made on Dobbie
Qty of Fabric 3 made on Dobbie
Qty of Fabric 4 made on Dobbie
Qty of Fabric 5 made on Dobbie
Qty of Fabric 3 made on Regular
Qty of Fabric 4 made on Regular
Qty of Fabric 5 made on Regular
Qty of Fabric 1 Purchased
Qty of Fabric 2 Purchased
Qty of Fabric 3 Purchased
Qty of Fabric 4 Purchased
Qty of Fabric 5 Purchased

Maximize Equation:
Profit Margin = Sum of (Qty of each Fabric on each machine*contribution margin) + Sum of (Qty of each Fabric Purchased*contribution margin) DOBBIE LOOM
FABRIC 1FABRIC 2FABRIC 3FABRIC 4FABRIC 5
CONTRIBUTION MARGIN0.330.310.610.730.2

REGULAR LOOM
FABRIC 3FABRIC 4FABRIC 5
CONTRIBUTION MARGIN0.610.730.2

PURCHASED FABRICS
FABRIC 1FABRIC 2FABRIC 3FABRIC 4FABRIC 5
CONTRIBUTION MARGIN0.190.160.50.540

Constraints:
Constraints are listed in a table at the end of the project. This is produced in table from the DS program and is difficult to decipher without the below explanations. Constraints 1-2:
We have been provided the amount of fabric in Yards/Hour. In order to use the information provided we need to convert this information to how many Hours it takes to create one yard of fabric. Summing the amount of each individual Loom contribution in Hours/Yard * The Qty of Yards/Month (Decision variables) will less than or equal to the amount of Hours/Month available. Dobbie hours available for the month = 8 machines * 24 Hours * 30 Days = 5760 hours/month Regular hours available for the month = 30 machines * 24 Hours * 30 Days = 21,600 hours/month

Constraints 3-7:
The total amount of each individual Fabric totals cannot exceed the demand for each of the fabrics.

Solutions:

Question 1:
Final...
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