A pottery company produces three types of products from clay: dining ware,

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?