HElp!! Case Problem: Saudi Tiles, Ltd. Hafiz and Nahla spent several summers dur
ID: 3209833 • Letter: H
Question
HElp!!
Case Problem: Saudi Tiles, Ltd. Hafiz and Nahla 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 from local artisans. After college they made use of their college experiences to start a tile manufacturing firm called Saudi 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. Hafiz and Nahla plan to produce two basic types of tile for use in home bathrooms, kitchens, sunrooms, and laundry rooms. The two types of tile 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 hour for a batch of 100 larger tiles and 0.58 hour 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 hour for a batch of 100 larger tiles and 0.20 hour 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. Saudi
Explanation / Answer
a) Linear programming model for mosaic tiles Ltd:
Maximize Z = 190x1 + 240x2
Subject to
0.30x1 + 0.25x2 60 hr.- molding
0.27x1 + 0.58x2 105 hr.- baking
0.16x1 + 0.20x2 40 hr.-glazing
32.8x1 + 20x2 6,000 lb.-clay
x1,x2 0
b) Maximize Z =190x1 + 240x2 + 0s1 + 0s2 + 0s3 + 0s4
subject to
0.30x1 + 0.25x2 + s1 = 60
0.27x1 + 0.58x2 + s2 = 105
0.16x1 + 0.20x2 + s3 = 40
32.8x1 + 20x2 + s4 = 6000
x1,x2,s1,s2,s3,s4 0
c) Plotting linear programming graphically in solver will get following points :
A: x1 = 0, x2 = 181.103, Z = $43447.20
B : x1 = 56.70, x2 =154.64, Z = $47886.60
C : x1 = 100, x2 = 120,Z = $47800
D : x1=136.36, x2 = 76.36, Z = 44234.80
E: x1 = 182.93, x2 =0, Z = 34756.70
Optimal solution point is B
d) Resources not used at optimal point
x1 = 56.70, x2 = 154.64
0.30(56.7) + 0.58(154.64) + s1 = 60
s1 = 4.33 hrs of moulding time
0.27(56.7) + 0.58(154.64) + s2 = 105
s2 = 0 hrs of baking time
0.16(56.7) + 0.20(154.64) + s3 = 40
s3 = 0 hrs of glazing time
32.8(56.7) + 20(154.64) + s4 = 6000
s4 = 1047.4 lbs of clay
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