a. In Problem 50, if the pottery company determines that the profit from dining ware was £15 instead of £10, how does that affect the optimal solution?
b. If the pottery company could secure additional resources, either clay or oven capacity or wheel time, which would you recommend to secure and how much of it? 

c. If the pottery company plans to reduce either the stock of clay by 40 kg or the oven capacity by 40 units, which will you recommend?
d. If the company expects that the sales of tiles will not exceed one-third of the sales of other two types of products, will the new profit be the same?

Data From Problem 50

A pottery company produces three types of products from clay: dining ware, sanitary ware, and floor  tiles. The company has a stock of 500 kg of clay. A dining ware needs 2 kg of clay, sanitary ware, 4 kg, and tiles, 1 kg. The oven has space for 200 items for the heating process during production. A potter’s  wheel creates molds for these products. Dining ware needs 12 minutes of wheel’s time, sanitary ware, 14 minutes, and tiles, 10 minutes. Potter’s wheel has 2,000 hours of processing time. The company  expects that the sales of tiles will not exceed half of the sales of other two types of products. The firm  expects a profit of £10 from dining ware, £13 from sanitary ware, and £18 from floor tiles.  

a. Formulate a liner programming model to find the optimal product mix to maximize profit.
b. What is the optimal solution?