d Angela Pasaic spent e Southwest. While at the ey made use of their co Opened their plant in Ne Ouse to make a clay deriv

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Create a step-by-step excel, using the solver engine to generate the decision variable
solution. Generate an ANSWER REPORT and a SENSITIVITY REPORT. I WILL UPVOTE. THANK YOU

CASE 1. Mossaic Tiles, Ltd.
Gilbert Moss and Angela Pasaic spent several summers during their college years working at
archaeological sites in the Southwest. While at those digs, they learned how to make ceramic tiles from local
artisans. After college they made use of their college experiences to start a tile manufacturing firm called
Mossaic Tiles, Ltd. They opened their plant in New Mexico, where they would have convenient access to a
special clay they intend to use to make a clay derivative for their tiles. Their manufacturing operation consists
of a few relatively simple but precarious steps, including molding the tiles, baking, and glazing.
Gilbert and Angela plan to produce two basic types of tile for use in home bathrooms, kitchens,
sunrooms, and laundry rooms. The two types of tile are a larger, single-colored tile and a smaller, patterned
tile. In the manufacturing process, the color or pattern is added before a tile is glazed. Either a single color is
sprayed over the top of a baked set of tiles or a stenciled pattern is sprayed on the top of a baked set of tiles.
The tiles are produced in batches of 100. The first step is to pour the clay derivative into specially
constructed molds. It takes 18 minutes to mold a batch of 100 larger tiles and 15 minutes to prepare a mold
for a batch of 100 smaller tiles. The company has 60 hours available each week for molding. After the tiles
are molded, they are baked in a kiln: 0.27 hour for a batch of 100 larger tiles and 0.58 hour for a batch of 100
smaller tiles. The company has 105 hours available each week for baking. After baking, the tiles are either
colored or patterned and glazed.
This process takes 0.16 hour for a batch of 100 larger tiles and 0.20 hour for a batch of 100 smaller
tiles. Forty hours are available each week for the glazing process. Each batch of 100 large tiles requires 32.8
pounds of the clay derivative to produce, whereas each batch of smaller tiles requires 20 pounds. The
company has 6,000 pounds of the clay derivative available each week.
Mossaic Tiles earns a profit of $190 for each batch of 100 of the larger tiles and $240 for each batch
of 100 smaller patterned tiles. Angela and Gilbert want to know how many batches of each type of tile to
produce each week to maximize profit. In addition, they have some questions about resource usage they
would like answered.
Required:
1. Formulate a linear programming model for Mossaic Tiles, Ltd., and determine the mix of tiles it should
manufacture each week using the computer.
2. Determine the resources left over and not used at the optimal solution point.
3. Determine the sensitivity ranges for the objective function coefficients and constraint quantity values.
Transcribed Image Text:CASE 1. Mossaic Tiles, Ltd. Gilbert Moss and Angela Pasaic spent several summers during their college years working at archaeological sites in the Southwest. While at those digs, they learned how to make ceramic tiles from local artisans. After college they made use of their college experiences to start a tile manufacturing firm called Mossaic Tiles, Ltd. They opened their plant in New Mexico, where they would have convenient access to a special clay they intend to use to make a clay derivative for their tiles. Their manufacturing operation consists of a few relatively simple but precarious steps, including molding the tiles, baking, and glazing. Gilbert and Angela plan to produce two basic types of tile for use in home bathrooms, kitchens, sunrooms, and laundry rooms. The two types of tile are a larger, single-colored tile and a smaller, patterned tile. In the manufacturing process, the color or pattern is added before a tile is glazed. Either a single color is sprayed over the top of a baked set of tiles or a stenciled pattern is sprayed on the top of a baked set of tiles. The tiles are produced in batches of 100. The first step is to pour the clay derivative into specially constructed molds. It takes 18 minutes to mold a batch of 100 larger tiles and 15 minutes to prepare a mold for a batch of 100 smaller tiles. The company has 60 hours available each week for molding. After the tiles are molded, they are baked in a kiln: 0.27 hour for a batch of 100 larger tiles and 0.58 hour for a batch of 100 smaller tiles. The company has 105 hours available each week for baking. After baking, the tiles are either colored or patterned and glazed. This process takes 0.16 hour for a batch of 100 larger tiles and 0.20 hour for a batch of 100 smaller tiles. Forty hours are available each week for the glazing process. Each batch of 100 large tiles requires 32.8 pounds of the clay derivative to produce, whereas each batch of smaller tiles requires 20 pounds. The company has 6,000 pounds of the clay derivative available each week. Mossaic Tiles earns a profit of $190 for each batch of 100 of the larger tiles and $240 for each batch of 100 smaller patterned tiles. Angela and Gilbert want to know how many batches of each type of tile to produce each week to maximize profit. In addition, they have some questions about resource usage they would like answered. Required: 1. Formulate a linear programming model for Mossaic Tiles, Ltd., and determine the mix of tiles it should manufacture each week using the computer. 2. Determine the resources left over and not used at the optimal solution point. 3. Determine the sensitivity ranges for the objective function coefficients and constraint quantity values.
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