Each question in Assignment 2 is worth 20 marks. For each question, do the following: (a) Formulate a model for the problem either in LINGO syntax or an Excel file. 1 For each model: (i) Write your name and student number. (ii) Write the definitions of all the variables. (This is the same as what was given for Q1; make your own variable definitions for the other questions.) (iii) Write the objective function. (iv) Write the constraints with comments to explain their purpose. 2 (v) The non-negativity restrictions are to be omitted. 3 (vi) LINGO only: Every variable which must be integer must be so declared using an @GIN command. This is followed by an END command. Copy-and-paste the LINGO file into the Word or pdf submission document. (vii) Excel only: The Solver Parameters box must be filled in, including an int declaration for each integer variable. Copy-and-paste the Excel file into the Word or pdf submission document, and include a screenshot of the Solver Parameters box into this document. (b) Solve the model, and copy-and-paste either the LINGO solution file or the Excel Solver Answer Report into the Word or pdf submission document. (c) State the solution in words in the Word or pdf submission document. When you attempt to solve these models, you might receive a message about the solution being infeasible. While this is a theoretical possibility, it won't happen for any of hese questions. It would mean that a mistake has been made in formulating the model. 3. A company makes robots, mostly for industrial use, but as a novelty item they also make robotic pets. These robotic cats and dogs are not aimed at children, but due to their high cost of production the target market is seniors, who are now in a retirement home and cannot have a living pet. One of their products is a calico cat, which in addition to purring and meowing, can twist her head, lick her paw, and roll over onto her side. They have received orders for units of this cat six months in advance of the desired delivery. Hence the company knows that the demand over the next six months will be: It is now December 1. Based on what has already been planned for this month, the inventory of this robotic cat as of December 31 will be 800 units. Up to 5000 units can be manufactured each month based on each employee working on regular time. Each cat costs $120 if manufactured on regular time. It is also possible to manufacture up to 1200 robotic calico cats per month on overtime. Each cat so produced would cost $170. Robotic pets can be kept in inventory at a cost of $5 per robot per month. This charge represents the cost of tied-up capital, warehouse, and insurance expenses. As a buffer against potentially high demand at the end of the planning horizon, the ending inventory should be at least 500 units. Back-ordered units are permitted (see Section 3.3.2 of the textbook), but at a penalty cost of $40 per robotic pet per month. We wish to formulate a model which seeks to minimize the sum of production costs. inventory holding costs, and back-order penalty costs