Makelt company produces three products from raw material. thirty thousand pounds of raw material is available. each pound of raw material can be transformed into 0.4 pounds of product 1, 0.3 pounds of product 2, and 0.2 pounds of product 3, while 0.1 pounds is lost as waste material. in addition, each pound of product 1 can be used to produce 0.6 pounds of product 2, 0.3 pounds of product 3, and 0.1 pounds of waste material; this pound of product 1 cannot be sold later. assuming that there are enough available resources to make the necessary amount of each product, formulate and solve a linear program that allows makeit to sell at least 4000 pounds of product 1, 8000 pounds of product 2, and 10,000 pounds of product 3 while minimizing the total amount of waste material produced?