For problems 1 and 2 below, develop a mathematical programming formulation. State whether your formulation is an LP, IP, MIP, or NLP and explain why. Problem 1. A factory is building a 500-square feet open rectangular cooling pool for water exhausted from its main process. The pool will be 8 feet deep, its length should be at least twice its width, and there is room for a width of at most 15 feet. We wish to choose the feasible design that minimizes cost by minimizing the concrete area of the pool walls. Problem 2. A company will manufacture a product for the next four months. The demands for each month are 550, 750, 550, and 650 units, respectively. The company has a steady workforce of 10 employees but can meet fluctuating production needs by hiring and firing temporary workers, if necessary. The extra costs of hiring and firing in any month are $300 and $600 per worker respectively. A permanent worker can produce 15 units per month, and a temporary worker, lacking comparable experience, only produces 10 units per month. The company can produce more than needed any month and carry the surplus over to a succeeding month at a holding cost of $20 per unit per month. Formulate a mathematical program to find the optimal hiring/firing policy for the company over the four-month planning horizon