Gilbert Moss and Angela Pasaic spent several summers duringtheir college years working at archaeological sites in theSouthwest. While at those digs, they learned how to make ceramictiles from local artisans. After college they made use of theircollege experiences to start a tile manufacturing firm calledMossaic Tiles, Ltd. They opened their plant in New Mexico, wherethey would have convenient access to a special clay they intend touse to make a clay derivative for their tiles. Their manufacturingoperation consists of a few relatively simple but precarious steps,including molding the tiles, baking, and glazing. Gilbert andAngela plan to produce two basic types of tile for use in homebathrooms, kitchens, sunrooms, and laundry rooms. The two types oftile are a larger, single- colored tile and a smaller, patternedtile.In the manufacturing process, the color or pattern is addedbefore a tile is glazed. Either a single color is sprayed over

the top of a baked set of tiles or a stenciled pattern issprayed on the top of a baked set of tiles.The tiles are producedin batches of 100. The first step is to pour the clay derivativeinto

specially constructed molds. It takes 18 minutes to mold a batchof 100 larger tiles and 15 minutes to prepare a mold for a batch of100 smaller tiles. The company has 60 hours available

each week for molding. After the tiles are molded, they arebaked in a kiln: 0.27 hour for a batch of 100 larger tiles and 0.58hour for a batch of 100 smaller tiles. The company has 105hours

available each week for baking. After baking, the tiles areeither colored or patterned and glazed. This process takes 0.16hour for a batch of 100 larger tiles and 0.20 hour for a batch of100

smaller tiles. Forty hours are available each week for theglazing process. Each batch of 100 large tiles requires 32.8 poundsof the clay derivative to produce, whereas each batch ofsmaller

tiles requires 20 pounds. The company has 6,000 pounds of theclay derivative available each week. Mossaic Tiles earns a profitof $190 for each batch of 100 of the larger tiles and $240 for

each batch of 100 smaller patterned tiles. Angela and Gilbertwant to know how many batches of each type of tile to produce eachweek to maximize profit. In addition, they have some questionsabout resource usage they would like answered.

A) Formulate a linear programming model on excel for MossaicTiles, Ltd. to determine the mix of tiles it should manufactureeach week.

B) For artistic reasons, Gilbert and Angela like to produce thesmaller, patterned tiles better. They also believe that in the longrun, the smaller tiles will be a more successful product.

What must the profit be for the smaller tiles in order for thecompany to produce only the smaller tiles?

C) Mossaic believes it may be able to reduce the time requiredfor molding to 16 minutes for a batch of larger tiles and 12minutes for a batch of the smaller tiles. How will this affect

the solution?

D) The company that provides Mossaic with clay has indicatedthat it can deliver an additional 100 pounds each week. ShouldMossaic agree to this offer? Explain.