1. Natural Oats is selling bushels of oats to food processing plants, and is trying to determine how many bushels it should produce and sell over the next two years. If the company produces an million bushels during year 1I each bushel can be sold for $(4U x. ). If the company produces 32 million bushels during year 2, each bushel can be sold for 3(45 $2). The cost of growing rl million bushels in year 1 is [1.53% million dollars, and the cost of growing 3:; million bushels in year 2 is 23:; million dollars. No more than 35 million bushels may be produced, at most $250 million can be spent on production, and no more than 40% of total production over the two years may occur during year 2. (a) Formulate a nonlinear programming problem (NLP) to help Natural Oats max- imize prots (revenues - costs) for the next tw0 years subject to the stated con- straints. Provide descriptive labels for the functional constraints. (b) Which of the four main assumptions of linear programming does the model you created in part (a) violate? Explain. (c) What additional assumptions {if any) are you making in your formulation in part (a)