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Mossiac Tiles, Ltd: Linear Programming Model




Question;Mossiac Tiles, Ltd: Linear Programming Model;Mossiac Tiles, Ltd.;a. Formulate;a linear programming model for Mossaic Tiles Ltd. and determine the mix of the;tiles it should manufacture each week.;b. Transform;the model into standard form.;c. Solve;the linear programming model graphically. (Ignore this Problem);d. Determine;the resources left over and not used at the optimal solution point.;e. Determine;the sensitivity ranges for the objective function coefficients and constraint;quantity values using the graphical solution of the model.;f. For;artistic reasons Gilbert and Angela like to produce the smaller, patterned;tiles better. They also believe in the long run the smaller tiles will be a;more successful product. What must the profit be for the smaller tiles in order;for the company to produce only the smaller tiles?;g. Solve the;linear programming model using the computer and verify the sensitivity ranges;computed in (E).;h. Mossaic;believes it may be able to reduce the time required for molding to 16 minutes;for a batch of larger tiles and 12 minutes for a batch of the smaller tiles.;How will this affect the solution?;i. The;company that provides Mossaic with clay has indicated that it can deliver an;additional 100 pounds each week. Should Mossaic agree to this offer?;j. Mossaic;is considering adding capacity to one of its kilns to provide 20 additional;glazing hours per week at a cost of $90,000. Should it make the investments?;k. The kiln;for glazing had to be shut down for 3 hours reducing the available kiln hours;from 40 to 37. What effect will this have on the solution?;Case;Gilbert Moss and Angela Pasaic spent several summers during;their college years working at archaeological sites in the Southwest. While at;these 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 titles 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 l00 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 had 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 to maximize profit. In addition, they also have some questions;about resource usage they would like answered.


Paper#60305 | Written in 18-Jul-2015

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