A) 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 contributions to profit. The following information shows the percentage of materials needed for each grade and the profit per square foot.

	Grade I	Grade II	Grade III
Profit/square foot	$2.50	$4.00	$5.00
Clay	50%	30%	25%
Silica	5%	15%	10%
Sand	20%	15%	15%
Feldspar	25%	40%	50%

Each week, Sanford Tile receives raw-material shipments, and the operations manager must schedule the plant to efficiently use the materials to maximize profitability. Currently, inventory consists of 6,000 pounds of clay, 3,000 pounds of silica, 5,000 pounds of sand, and 8,000 pounds of feldspar. Because demand varies for the different grades, marketing estimates that at least 100 square feet of Grades I, II and III tiles are required. Each square foot of tile weighs approximately 2 pounds. Develop and solve a linear optimization model using Excel Solver. How many of each grade of tile the company should make next week to maximize profit contribution, and what is the profit?

B) With the same set-up as above question, but marketing estimates that at least 200 square feet of Grades I, 100 square feet of Grades II and III tiles are required. Answer the question without solving a new linear program. How would the optimal profit and optimal solution change? You might need to use auxiliary variable in the linear program and get your answers from the Sensitivity Report.