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Home Q & A Board Science-Related Homework Help Mathematics Statistics and Probability
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malabranche13 malabranche13
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4 years ago
Use the scenario below to answer the following question(s).

A company makes standard 115-inch-wide rolls of thin sheet metal, and slits them into smaller rolls to meet customer orders for widths of 13, 16, and 25 inches. The demands for these widths vary from week to week. From a 115-inch roll, there are many different ways to slit 13-, 16-, and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock. Of course, one would want to use as much of the roll as possible to avoid costly scrap. For example, one could cut seven 16-inch rolls, leaving a 3-inch piece of scrap. Finding good cutting patterns for a large set of end products is in itself a challenging problem. Suppose that the company has proposed the following cutting patterns:



Demands this week are 1,000 13-inch rolls, 1,430 16-inch rolls, and 1,260 25-inch rolls. The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define Xi to be the number of 115-inch rolls to cut using cutting pattern i, for i = 1, …, 6.
Note that Xi needs to be a whole number because each roll that is cut generates a different number of end items.


Determine the objective function.

▸ Maximize 1X1 + 8X2 + 2X3 + 6X4 + 3X5 + 4X6

▸ Maximize 1,000X1 + 1,430X2 + 1,260X3

▸ Minimize 3X1 + 8X2 + 2X3 + 11X4 + 7X5 + 5X6

▸ Minimize 3X2 + 4X3 + 2X5
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Statistics, Data Analysis, and Decision Modeling

Statistics, Data Analysis, and Decision Modeling


Edition: 5th
Author:
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bli14bli14
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#1
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4 years ago
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#2
4 years ago
Use the scenario below to answer the following question(s).

A company makes standard 115-inch-wide rolls of thin sheet metal, and slits them into smaller rolls to meet customer orders for widths of 13, 16, and 25 inches. The demands for these widths vary from week to week. From a 115-inch roll, there are many different ways to slit 13-, 16-, and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock. Of course, one would want to use as much of the roll as possible to avoid costly scrap. For example, one could cut seven 16-inch rolls, leaving a 3-inch piece of scrap. Finding good cutting patterns for a large set of end products is in itself a challenging problem. Suppose that the company has proposed the following cutting patterns:



Demands this week are 1,000 13-inch rolls, 1,430 16-inch rolls, and 1,260 25-inch rolls. The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define Xi to be the number of 115-inch rolls to cut using cutting pattern i, for i = 1, …, 6.
Note that Xi needs to be a whole number because each roll that is cut generates a different number of end items.


Identify the constraint specified for 13-inch rolls.

▸ 2X2 + 6X4 + 2X5 + 7X6 ≥ 1,430

▸ X3 + 8X4 + 2X5 + 6X6 ≥ 1,000

▸ X2 + 4X4 + X5 + 3X6 ≤ 500

▸ 7X2 ≤ 1,000
wrote...
#3
4 years ago
X3 + 8X4 + 2X5 + 6X6 ≥ 1,000
wrote...
#4
4 years ago
Use the scenario below to answer the following question(s).

A company makes standard 115-inch-wide rolls of thin sheet metal, and slits them into smaller rolls to meet customer orders for widths of 13, 16, and 25 inches. The demands for these widths vary from week to week. From a 115-inch roll, there are many different ways to slit 13-, 16-, and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock. Of course, one would want to use as much of the roll as possible to avoid costly scrap. For example, one could cut seven 16-inch rolls, leaving a 3-inch piece of scrap. Finding good cutting patterns for a large set of end products is in itself a challenging problem. Suppose that the company has proposed the following cutting patterns:



Demands this week are 1,000 13-inch rolls, 1,430 16-inch rolls, and 1,260 25-inch rolls. The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define Xi to be the number of 115-inch rolls to cut using cutting pattern i, for i = 1, …, 6.
Note that Xi needs to be a whole number because each roll that is cut generates a different number of end items.


The constraint for 16-inch rolls is formulated as ________.

▸ X1 + X2 + X5 + X6 ≤ 715

▸ 7X1 + 2X2 + 2X5 + 2X6 ≥ 1,430

▸ 3X2 + 4X3 + 2X5 ≤ 1,430

▸ 2X2 + 6X3 + 5X4 ≥ 715
wrote...
#5
4 years ago
7X1 + 2X2 + 2X5 + 2X6 ≥ 1,430
wrote...
#6
4 years ago
Use the scenario below to answer the following question(s).

A company makes standard 115-inch-wide rolls of thin sheet metal, and slits them into smaller rolls to meet customer orders for widths of 13, 16, and 25 inches. The demands for these widths vary from week to week. From a 115-inch roll, there are many different ways to slit 13-, 16-, and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock. Of course, one would want to use as much of the roll as possible to avoid costly scrap. For example, one could cut seven 16-inch rolls, leaving a 3-inch piece of scrap. Finding good cutting patterns for a large set of end products is in itself a challenging problem. Suppose that the company has proposed the following cutting patterns:



Demands this week are 1,000 13-inch rolls, 1,430 16-inch rolls, and 1,260 25-inch rolls. The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define Xi to be the number of 115-inch rolls to cut using cutting pattern i, for i = 1, …, 6.
Note that Xi needs to be a whole number because each roll that is cut generates a different number of end items.


Determine the constraint modeled for 25-inch rolls.

▸ 7X2 + X3 ≤ 630

▸ X2 + 2X3 + X4 ≥ 630

▸ 3X2 + 4X3 + 2X5 ≥ 1,260

▸ 3X1 + 8X2 + 2X3 + 11X4 + 7X5 + 5X6 ≥ 1,260
wrote...
#7
4 years ago
3X2 + 4X3 + 2X5 ≥ 1,260
wrote...
#8
4 years ago
Use the scenario below to answer the following question(s).

A company makes standard 115-inch-wide rolls of thin sheet metal, and slits them into smaller rolls to meet customer orders for widths of 13, 16, and 25 inches. The demands for these widths vary from week to week. From a 115-inch roll, there are many different ways to slit 13-, 16-, and 25-inch pieces.
A cutting pattern is a configuration of the number of smaller rolls of each type that are cut from the raw stock. Of course, one would want to use as much of the roll as possible to avoid costly scrap. For example, one could cut seven 16-inch rolls, leaving a 3-inch piece of scrap. Finding good cutting patterns for a large set of end products is in itself a challenging problem. Suppose that the company has proposed the following cutting patterns:



Demands this week are 1,000 13-inch rolls, 1,430 16-inch rolls, and 1,260 25-inch rolls. The problem is to develop a model that will determine how many 115-inch rolls to cut into each of the six patterns in order to meet demand and scrap.
Define Xi to be the number of 115-inch rolls to cut using cutting pattern i, for i = 1, …, 6.
Note that Xi needs to be a whole number because each roll that is cut generates a different number of end items.


If the demand for the 25-inch rolls increases to 1,300, the total scrap value ________.

▸ decreases by 6 units

▸ does not show an increase or a decrease

▸ increases by 13 units

▸ increases by 40 units
wrote...
#9
4 years ago
increases by 13 units
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