Note: Borderline fails in this course are determined when the final overall mark is in the range 45-49 inclusive.
Please note that:
• Both assignments must be accompanied by an Assignment Cover Sheet. • Both assignments must be submitted electronically through Grade Centre in Blackboard with a Turnitin report attached. This provides us with evidence of the time and date of submission. • Hard copies of both assignments must also be submitted on the due date in the Lecture. All assignments are to be word-processed. Don’t send your assignments by email. • Assessment tasks may be varied with the documented consent of 70% of students enrolled in the course. • The assessed assignments will be returned to students within two weeks of the due date. • For both Assignments (1 and 2) you MUST provide the mathematical formulation of the problem.
Assignment 1: Individual Assignment 20% Marks Due date: 23 August 2012 (no word limit) Case Study: Scottsville Textile Mill The Scottville 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 in Table 1, along with data on 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.
Table 1 Monthly Demand, selling proce, variable cost, amnnd purchsing price data Fabric | Demand (yards) | Selling Price($/yard) | variable cost ($/yard)| Purchase price ($/yard| 1 | 16500| 0.99| 0.66| 0.80|
2 | 22000| 0.86| 0.55| 0.70|
3 | 62000| 1.10| 0.49| 0.60|
4 | 7500| 1.24| 0.51| 0.70|
5 | 62000| 0.70| 0.50| 0.70|
The mill has two types of looms: the 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 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. Table 2 Loom Production Rates for The Scottsville Textile Mill Loom Rate (yards/hour) Fabric | Bobbie | Regular|
1 | 4.63| --|
2 | 4.63| --|
3 | 5.23| 5.23|
4 | 5.23| 5.23|
5 | 4.17| 4.17|
note: Fabrics 1 and 2 can be manufactired only on the dobbie loom.
The Scottville Textile Mill satisfies all demand with either its own fabric or fabric purchased from another mill. Fabrics that cannot be woven at the Scottville Textile Mill because of limited loom capacity will be purchased from another mill. The purchase price of each fabric is also shown in Table 1.
Develop a model that can be used to schedule production for Scottville Textile 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 report.
1. Provide the mathematical model for this problem.
2. The final production schedule and loom assignment for each fabric. 3. The projected total contribution to profit.
4. A discussion on 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?) 5. A discussion of...