A company makes ceramic and porcelain tiles. They produce three different grades of tile, each of which requires different amounts of materials and production time and generates different contributions to profit. The accompanying table shows the percentage of materials needed for each grade and the profit per square foot. Each week, the company receives raw material shipments, which must be used efficiently to maximize profitability. Currently, inventory consists of 6,000 pounds of clay, 3,500 pounds of silica, 5,000 pounds of sand, and 8,500 pounds of feldspar. At most 8,000 square feet of grade III tiles should be produced and at least 2,000 square feet of grade I tiles are required. Each square foot of tile weighs approximately 2 pounds. Develop and solve a linear optimization model to determine how many of each grade of tile the company should make next week to maximize profit contribution. Click here to view the tile data. Complete the table below to indicate the number of square feet of each tile to produce to optimize the profit, and then give the total profit earned. (Type integers or decimals, Do not round.) Grade I Square Feet to Produce CII Total Profit S Grade II Grade Ill

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Tile Production Data
Profit/square foot
Clay
Silica
Sand
Feldspar
Grade I
$2.50
50%
5%
20%
25%
Print
Grade II
$4.00
30%
15%
15%
40%
Done
Grade Ill
$6.00
25%
10%
15%
50%
0
-
Transcribed Image Text:Tile Production Data Profit/square foot Clay Silica Sand Feldspar Grade I $2.50 50% 5% 20% 25% Print Grade II $4.00 30% 15% 15% 40% Done Grade Ill $6.00 25% 10% 15% 50% 0 -
A company makes ceramic and porcelain tiles. They produce three different grades of tile, each of which requires
different amounts of materials and production time and generates different contributions to profit. The accompanying
table shows the percentage of materials needed for each grade and the profit per square foot. Each week, the company
receives raw material shipments, which must be used efficiently to maximize profitability. Currently, inventory consists of
6,000 pounds of clay, 3,500 pounds of silica, 5,000 pounds of sand, and 8,500 pounds of feldspar. At most 8,000 square
feet of grade III tiles should be produced and at least 2,000 square feet of grade I tiles are required. Each square foot of
tile weighs approximately 2 pounds. Develop and solve a linear optimization model to determine how many of each
grade of tile the company should make next week to maximize profit contribution.
Click here to view the tile data.
Complete the table below to indicate the number of square feet of each tile to produce to optimize the profit, and then
give the total profit earned.
(Type integers or decimals, Do not round.)
Grade I
Square Feet to Produce
Total Profit=$
Grade II
O
Grade Ill
Transcribed Image Text:A company makes ceramic and porcelain tiles. They produce three different grades of tile, each of which requires different amounts of materials and production time and generates different contributions to profit. The accompanying table shows the percentage of materials needed for each grade and the profit per square foot. Each week, the company receives raw material shipments, which must be used efficiently to maximize profitability. Currently, inventory consists of 6,000 pounds of clay, 3,500 pounds of silica, 5,000 pounds of sand, and 8,500 pounds of feldspar. At most 8,000 square feet of grade III tiles should be produced and at least 2,000 square feet of grade I tiles are required. Each square foot of tile weighs approximately 2 pounds. Develop and solve a linear optimization model to determine how many of each grade of tile the company should make next week to maximize profit contribution. Click here to view the tile data. Complete the table below to indicate the number of square feet of each tile to produce to optimize the profit, and then give the total profit earned. (Type integers or decimals, Do not round.) Grade I Square Feet to Produce Total Profit=$ Grade II O Grade Ill
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