Expert answer:Linear Programming Case Study

Expert answer:It will be a problem with at least three (3) constraints and at least two (2) decision variables. The problem will be bounded and feasible. It will also have a single optimum solution (in other words, it won’t have alternate optimal solutions). The problem will also include a component that involves sensitivity analysis and the use of the shadow price.You will be turning in two (2) deliverables, a short writeup of the project and the spreadsheet showing your work.Writeup.Your writeup should introduce your solution to the project by describing the problem. Correctly identify what type of problem this is. For example, you should note if the problem is a maximization or minimization problem, as well as identify the resources that constrain the solution. Identify each variable and explain the criteria involved in setting up the model. This should be encapsulated in one (1) or two (2) succinct paragraphs.After the introductory paragraph, write out the L.P. model for the problem. Include the objective function and all constraints, including any non-negativity constraints. Then, you should present the optimal solution, based on your work in Excel. Explain what the results mean.Finally, write a paragraph addressing the part of the problem pertaining to sensitivity analysis and shadow price.Excel.As previously noted, please set up your problem in Excel and find the solution using Solver. Clearly label the cells in your spreadsheet. You will turn in the entire spreadsheet, showing the setup of the model, and the results.Click here to view the grading rubric for this assignment.For this assignment, you must submit 2 files, an MS Word document that contains your write up and an Excel spreadsheet that shows your calculations. Please be sure to show all work. If you show answers but not how you arrived at your answers, you will not receive full credit.Your safe assign score should be no more than 15%.
week_8_case_problem_mossaic_tiles_2_.docx

student_template_key_week_8_case_problem_mossaic_tiles.xlsx

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Case Problem 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 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.
A. Formulate a linear programming model for Mossaic Tiles, Ltd
B. Solve the linear programming model by using the computer.
C. Include and discuss the sensitivity report and the analysis report. Discuss the shadow price.
D. 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 smaller tiles. How will this affect the solution?
E. 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?
Mossaic Tiles LTD
Products
Profit per unit
Resources
Molding
Baking
Glazing
Clay
Production
Large Tiles
Small Tiles
Profit
Week 8 Case
Large Tiles (x1) Small Tiles (x2)
Usage
0.27
0.58
32.8
20
Resources
Constraint
<= <= <= <= Available 60 105 40 6000 Left Over ... Purchase answer to see full attachment

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