1. A gas processing plant receives a fixed amount of raw gas each week. The raw gas is processed into 2 grades of heating gas, regular and premium quality. Only one of the grades can be produced at a time and the facility is open for only 80 hours/week. There is a limited on site storage for each of the products. Resource Product Resource availability Regular Premium Raw gas 7 m/ton 11 m/ton Production time 10 hr/ton 8 hr/ton Storage 9 tons 6 tons Profit $150/ton $175/ton 77 m /week 80 hr/week a. Build an optimization problem quoting objective function and constraints. (5 marks) b. Perform optimization using Simplex method. (15 marks)