Reference no: EM133087735

Standford Tile Companymakes 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 profitper 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 most 8,000 square feet of Grade III tile should be produced, and that at least 1,500 square feet of Grade I tile are required. Each square foot of tile weighs approximately 2 pounds.

1. Develop a linear optimization model and solve the model using QM for Windows to determine how many of each grade of tile the company should make next week to maximizeprofit contribution.

2. What happens if the profit on Grade I is increased by $0.05?

3. If an additional 500 pounds of feldspar is available, how will the optimal solution have affected?