(40 points) A manufacturer sells products A and B. Profit from A is $10/kg and from B $8/kg. Available raw materials for the products are: 100 kg of M1 and 80 kg of M2. To produce 1 kg of A, 0.4 kg of M1 and 0:6 kg of M2 are needed. To produce 1 kg of B, 0.5 kg of M1 and 0.5 kg of M2 are needed. Due to the market issue, the product amount should be limited to be less than or equal to 70 kg for A and 110 kg for B. 1. (9 points) Formulate the design optimization problem to determine how much of A and B should be produced to maximize profit subject to constraints. 2. (8 points) Formulate the problem in LP standard form. 3. (15 points) Solve the problem using the simplex method. 4. (8 points) Verify your solution graphically