Operations-Group Assignment 2

ASSIGNMENT 2:
Whitney Duckels, Justin Stuva, Angela Rice, Genelle Iocca

Mossaic Tiles, LTD.

Bilbert Moss and Angela
Pasaic spent several summers during their college years working at
archaeological sites in the Southwest. While at those digs, they
leaned how to make ceramic tiles from local artisns. After college
they made useof their college experiences to start a tile
manufacturing firm called Mossaic Tiles, Ltd. They opened their plant
in the new Mexico where they would have covenient access to a special
clay they intended to use to make a clay derivative for their tiles.
Their manufacturing operation consists of a few relatively simple bu
precarious steps, including molding the tiles, baking, and glazing.

Gilbert and Angela plan
to produce two basic types of tile for use in home bathrooms,
kitchens, sunrooms, and laundry rooms. The two types of tile are
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 constructred molds. It takes 18
minutes to mold for a batch of 100 larger tiles and 15 minutes to
prepare a mold for a batch of 100 smaller tiles. The cmpany
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 tles are eithercolored
or patterned and glazd. This process takes 0.16
hour for a batch of 100 larger ties and 0.20 hour for a batch of 100
smaller tiles. Forty hours are available each week for the blazing
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. Te company
has 6,000 pounds of the clay drivative availble each week.

Mosaic tiles earns a profit of $190 for each batch of 100 of the larger tiles
and $240 for each batch of 100 smaller pattered tiles. Angela
and Gilbert want to know how many batches of each type of tile to
produce each week to maximize profit. In addition, they have some
questions bout resource usage they would like answered.

1. Formulate a
linear programming model for Mosaic Tiles, Ltd., and determine the
mix of tiles it should manufactured each week. The formulation
process should be similar to lecture 3 from the class.

Maximum Profit=190L +240S

Subject to:

18L +15S <= 3,600 minutes

.27L + .58S <= 105hours .16L+ .20S <= 40 hours 32.8L + 20S <=6,000 pounds

2. Model the Linear
Programming model in Excel, and solve the LP problem. Generate
Solution, Sensitivity and Limit Reports.

To maximize profit Mosaic Tiles would need to produce 57 batches of the large tiles and
155 batches of the small tiles. Total profit would be $47,886.60.

3. For artistic reasons, Gilbert and Angela like to produce the smaller, patterned
tiles better. They also believe that in the long run, the smaller
tiles will be a more successful product. What must the profit be for
the smaller tiles in order for the company to produce only the
smaller tiles?

At a batch profit of $240 for small tiles it is not more profitable ($43,448.28) to
produce only the small tiles than producing both tiles together.
However, if Mosaic Tiles were to increase the batch profit to $265
for the small tiles the total profit ($47,974.14) would exceed the
total profit ($47,886.60) for both tiles, making it a good business
decision for the company.

4. Mosaic believes it may be able to reduce the time required for molding to 16 minutes for a batch of larger tiles an 12 minutes for a batch of the smaller
tiles. How will this affect the solution?

Reducing the molding minutes for both the larger and smaller tiles does not change the
total profit at all. However, the slack for molding hours increases
by a little less than 600 minutes, or 10 hours.

5. Mosaic is
considering adding capacity to one of its kilns to provide 2
additional glazing hours per week, at a cost of $90,000. Should it
make the investment?

Yes, adding capacity to provide an additional 2 glazing hours per week would be a good
investment for Mosaic Tiles because this investment would increase
the total profit by $1,845.79/week which is enough to pay off the
extra capacity within 49 weeks (less than one year), provided that
the kiln’s expected life is greater than one year.

Taking into account the time value of money and interest rates, we found that the investment
should definitely be accepted at a rate of 6.5% or less because the
investment could be paid off in one year.