A small company named LogTransit has at present 3 manufacturing facilities (suppliers) called Suppliers \#1, \#2, and #3 to supply goods to its 3 retail stores (customers) named Customer A, B, and C. Due to customer demands at stores increasing, the company decided to build a new manufacturing facility (Supplier) that will have a capacity of 200 units per week. After screening many potential sites for the new facility, Toledo and Cincinnati have been determined to be the two leading candidate locations. Assume that from Suppliers to Customers will be the main determinant to determine which of the two locations to be selected as the new plant site. The following two tables provide information on i) the capacities of old suppliers and new supplier candidates; ii) The per unit Transportation cost from existing Suppliers to customers and per unit Transportation cost from the new candidate supplier location to customers, and 3) demands from customers and available capacity of each supplier. One of the most important tasks of this project is to determine which New Supplier locations will result in the smallest total transportation costs. LP formulation a. Give a summary of the project Problem: - Describe in WORDS what Decision you need to make, and criterion on which your decision is based, and how Linear Programming models can be used to help you make your decision. b. Formulate the project problem into TWO LP models. - To make the right decision for the project, you need to formulate TWO Linear Programming models. - You may only provide a complete and detailed LP formulation for only one of the models. For example, assuming "TOLEDO" is chosen as the new plant. Then, give brief explanations of the difference in LP model formulation when "CINCINNATT' is chosen as the new plant. c. Emportant A Linear Programming Model formulation should be a Mathematical Model that contains - Clearly defined decision variables - A linear function of the Objective - All constraints in the form of Linear inequalities/equalities for which your decision variables need to satisfy, including non-negativity constraints