The Lawson Fabric Mill Produces five different fabrics. Each fabric can be woven on one or more of the mill’s 36 looms. The sales department’s forecast of demand for the next month is shown in below 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. The mill has two types of looms: draw and regular. The draw 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 36 looms: 8 are draw and 28 are regular. The rate of production for each fabric on each type of loom is given in below Table 2. The time required to change over from producing one fabric to another is negligible and does not have to be considered. The Lawson Fabric Mill satisfies all demand with either its own fabric or fabric purchased from another mill. Fabrics that cannot be woven at the Lawson Fabric Mill because of limited loom capacity will be purchased from another mill. The purchase price of each fabric is also shown in Table 1. Table 1 Fabric Demand (£/yard) Selling Price (£/yard) Variable Cost (£/yard) Purchase Price (£/yard) 1 16,700 0.99 0.66 0.80 2 22,300 0.86 0.55 0.70 3 62,400 1.10 0.49 0.60 4 7,600 1.24 0.51 0.70 5 62,500 0.70 0.50 0.70
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The Lawson Fabric Mill Produces five different fabrics. Each fabric can be woven on one or more of the mill’s 36 looms. The sales department’s forecast of demand for the next month is shown in below 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. The mill has two types of looms: draw and regular. The draw 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 36 looms: 8 are draw and 28 are regular. The rate of production for each fabric on each type of loom is given in below Table 2. The time required to change over from producing one fabric to another is negligible and does not have to be considered.
The Lawson Fabric Mill satisfies all demand with either its own fabric or fabric purchased from another mill. Fabrics that cannot be woven at the Lawson Fabric Mill because of limited loom capacity will be purchased from another mill. The purchase price of each fabric is also shown in Table 1.
Table 1
|
Fabric |
Demand (£/yard) |
Selling Price (£/yard) |
Variable Cost (£/yard) |
Purchase Price (£/yard) |
|
1 |
16,700 |
0.99 |
0.66 |
0.80 |
|
2 |
22,300 |
0.86 |
0.55 |
0.70 |
|
3 |
62,400 |
1.10 |
0.49 |
0.60 |
|
4 |
7,600 |
1.24 |
0.51 |
0.70 |
|
5 |
62,500 |
0.70 |
0.50 |
0.70 |
Table 2
|
|
Loom Rate (yards/hour) |
|
|
Fabric |
Draw |
Regular |
|
1 |
4.62 |
- |
|
2 |
4.62 |
- |
|
3 |
5.21 |
5.21 |
|
4 |
5.21 |
5.21 |
|
5 |
4.15 |
4.15 |
Managerial Report:
Develop a model that can be used to schedule production for the Lawson Fabric 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.
- The final production schedule and loom assignments for each fabric
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