please form an NLP

Problem #3 Alpha Manufacturing has discontinued production of one family of products. This has created excess production capacity, which Alpha is considering devoting to the production of one or more of three new products (products 1, 2 and 3). The available weekly capacities on the plant's machines are as follows: 500 hours on their milling machines, 350 hours on their lathes, and 150 hours on their grinders. Each unit of product I would require 9 hours on the milling machine, 5 hours on the lathe, and 3 hours on the grinder The grinder is not needel for product 2, but each unit of product 2 would require 3 hours on the milling machine and 4 hours on the Inthe. The lathe is not needed for product 3, however each unit of product 3 would require 5 hours on the milling machine and 2 hours on the grinder. The estimated unit production costs for products 1, 2 and 3 are $25, $10, and $15, respectively. Demands for these products are assumed to reflect price elasticities, such that the amount that can be sold has an inverse relationship to the price charged. Marketing research has estimated that the prices required (in dollars) in order to be able to sell *), 19, and r3 units are (35+100x7)(15+40.x, t), and (20+50x3), respectively. Formulate an NLP that will determine how many units of each product Alpha Manufacturing should produce each week to maximize profit, and solve the NLP using GAMS (submit your GAMS file and provide details of the optimal solution). Problem #3 Alpha Manufacturing has discontinued production of one family of products. This has created excess production capacity, which Alpha is considering devoting to the production of one or more of three new products (products 1, 2 and 3). The available weekly capacities on the plant's machines are as follows: 500 hours on their milling machines, 350 hours on their lathes, and 150 hours on their grinders. Each unit of product I would require 9 hours on the milling machine, 5 hours on the lathe, and 3 hours on the grinder The grinder is not needel for product 2, but each unit of product 2 would require 3 hours on the milling machine and 4 hours on the Inthe. The lathe is not needed for product 3, however each unit of product 3 would require 5 hours on the milling machine and 2 hours on the grinder. The estimated unit production costs for products 1, 2 and 3 are $25, $10, and $15, respectively. Demands for these products are assumed to reflect price elasticities, such that the amount that can be sold has an inverse relationship to the price charged. Marketing research has estimated that the prices required (in dollars) in order to be able to sell *), 19, and r3 units are (35+100x7)(15+40.x, t), and (20+50x3), respectively. Formulate an NLP that will determine how many units of each product Alpha Manufacturing should produce each week to maximize profit, and solve the NLP using GAMS (submit your GAMS file and provide details of the optimal solution)