Gilbert Moss and Angela Pasaic 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 Mossaic 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. 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 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 build 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.

Mossaic Tiles earns a profit of $190 for each batch of 100 of the larger tiles and $240 for

each batch of 100 smaller patterned 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 about resource usage they would like answered.

k. The kiln for glazing had to be shut down for 3 hours, reducing the available kiln hours

from 40 to 37. What effect will this have on the solution?

l. What are the reduced costs for larger and smaller tiles? Explain.

how to explain the steps for part L