3. A chemical company has been given a contract to supply its product to an oil refinery for a 3-month period. The company shall supply 50 tons of its product at the end of the first month, 50 ton at the end of the second month, and 50 ton at the end of the third month. The cost ($) of producing the product for any month is (x + 1000) where x is ton of product. In any month i = {1, 2, 3}, the chemical company can produce more quantity of product and can carry them into a subsequent month by holding the product in an inventory. However, it costs $20 for each ton of product to hold in inventory. The inventory for the product in the first month is initially zero. Formulate an NLP (non-linear programming) problem with constraints and determine the optimum quantity of product to be produced by the chemical company in each of the three months that will minimize the total cost of production.