LINEAR PROGRAMMING Mosaic Tile Company plans to produce two basic types of tile for home use: a larger singlecolored tile and a smaller patterned tile. The tiles are produced in batches of 100. The first step is to pour the clay into molds. It takes 27 minutes (.45 hours) to mold a batch of larger tiles and 18 minutes (.30 hours) to mold a batch of smaller tiles. The company has 75 hours available each week for molding. After the tiles are molded, they are baked in a kiln -- .40 hours for a batch of 100 larger tiles and .60 hours for a batch of 100 smaller tiles. The company has 105 hours available each week for baking. After baking, the tiles are glazed, and this process takes .15 hours for a batch of 100 larger tiles, and .25 hours for a batch of 100 smaller tiles. 60 hours are available each week for the glazing process. Each batch of 100 large tiles requires 30 pounds of clay to produce, while each batch of smaller tiles requires 20 pounds of clay. The company has 6000 pounds of clay available each week. Mosaic Tile earns a profit of $190 for each batch of 100 larger tiles and $240 for each batch of 100 smaller tiles.

7a) How many batches of each type of tile should be produced to maximize profit?

7b) What is the maximum weekly Profit the company can earn?

7c) How many hours of Baking resources are left over / not used at the optimal solution point?

7d) How much would an additional hour of Molding add to the profit?

7e) For artistic reasons, Mosaics owner likes to produce the Smaller tiles best. She also believes in the long run that the Smaller tiles will be a more successful product. What must be the profit for the Smaller tiles in order for the company to produce only the Smaller tiles?

7f) The company that supplies Mosaic with clay has indicated that it can deliver an additional 100 pounds of clay each week. Should Mosaic agree to this offer?