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 form 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 tiles for use in home bathrooms, kitchens, sunrooms, and laundry rooms. The two types of tiles 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 hours for a batch of 100 larger tiles and 0.58 hours 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 hours for a batch of 100 larger tiles and 0.20 hours 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.

Linear Programming Project

Overview

For this assignment, your instructor will assign a linear programming project based on the following specifications:

• It will be a problem with at least three constraints and at least two 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.

Instructions

You will be turning in two 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 or two succinct paragraphs.
• After the introductory paragraph, write out the LP 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.

Spreadsheet

Please set up your problem in QM for Windows or 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.

This course requires the use of Strayer Writing Standards. For assistance and information, please refer to the Strayer Writing Standards link in the left-hand menu of your course. Check with your professor for any additional instructions.

The specific course learning outcome associated with this assignment is:

• Determine an approach to a problem that uses a linear programming model.

****Please do in excel and send me the excel document, I'm so confused with the spreadsheet section****