# Sandford Tile Case Study: Linear Optimization Problem

Sandford Tile company makes ceramic and porcelain tile for residentail and commercial use. They produce three different grades of tile for walls, residential flooring, and commercial flooring each of which requires different amounts of materials and production time and generates different contribution to profit. The spreadsheet shows the percentage of materials needed for each grade and the profit per square foot. Each week Sandford tile receives raaw materials shipments and the operations manager must schedule the plan to efficiently use the matierals to maximize profitability. Currently inventory consists of 6000 pounds of clay, 3000 pounds of silica, 5000 pounds of sand, and 8000 pounds of Feldspar. Because demand varies for the different grades marketing estimates that at most 8000 square feet of grade III tile should be produced and that at east 1500 square feet of grade i tiles are required. Each square foot of tile weighs two pounds.

1. Develop a linear optimization model to determine how many of each grade of tile the company should make next week to maximize profit.

2. Implement the model on a spreadsheet and find an optimal solution

3. Explain the sensitivity information for the objective soefficients. What happens in the projit on Grade I is increased by $.05?

4. If an additional 500 pounds of feldspar is available how will the optimal solution be affected?

5. 1,000 pounds of clay are found to be of poor quality, what should the company do?

6. Use the auxilary variable cells technique to handle the bound contraints and generate all shadow prices.

https://brainmass.com/statistics/correlation-and-regression-analysis/sandford-tile-case-study-linear-optimization-problem-458121

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Linear Programming Model

"Sandford Tile company makes ceramic and porcelain tile for residential and commercial use. They produce three different grades of tile for walls, residential flooring, and commercial flooring each of which requires different amounts of materials and production time and generates different contribution to profit. The spread sheet shows the percentage of materials needed for each grade and the profit per square foot. Each week Sandford tile receives raw materials shipments and the operations manager must schedule the plan to ...

#### Solution Summary

The expert examines linear optimization problems for Sanford Tile Case Study.