2. Linear Optimization I (60 points) A plant can manufacture four products, A, B, C and D. The plant consists of three work areas: the material processing area St, the manufacturing area S; and the assembling area 83. The time (in hours) required to process one unit of each product in the three work areas are listed in the following table. The weekly capacity of work area S], S; and 53 are 12 hours, 15 hours and 20 hours, respectively. The plant can sell all its produces of these four products for a prot of S, 8, 4, 0.5 k$funit, respectively. We want to optimize the amounts (units) of each product to produce for a week, in order to maximize the plant's weekly prot. Formulate the optimization problem and use the Simplex algorithm to solve this problem. The amountsr'units of each product can be treated as continuous variables