Problem 1. (1.2 from text) A manufacturer of plastics is planning to blend a new product from four chemical compounds. These compounds are mainly composed of three elements: A, B, and C. The composition and unit cost of these chemicals are shown in the following table: CHEMICAL COMPOUND 2 3 Percentage A 35 15 35 25 Percentage B 20 65 35 40 Percentage C 40 15 25 30 Cost/kilogram 20 30 20 15 The new product consists of 25 percent element A, at least 35 percent element B, and at least 20 percent element C. Owing to side effects of compounds 1 and 2, they must not exceed 25 percent and 30 percent of the content of the new product. Formulate the problem of finding the least costly way of blending as a linear program