Question 1 Many of today's digital or electronic devices and equipment cannot function without the use of highly complex interconnected network of generally microscopic electronic components. Nano Semicon is one of the leading contract manufacturer of integrated circuits (or IE chips) manufacturer in the region. The worldwide shortage of these IC' chips has put pressure on IE chip manufacturers ever increasing demands. Nano Semicon currently manages to cope with this upsurge in IC chips consumption. Nano Semicon has already converted much of its manufacturing facility into a highly automated factory. employing robotics and articial intelligence to handle most of the repetitive tasks. However. the factory still needs some workers to be working in shifts such as process engineers. technical support personnel. software programmers and quality control inspectors. The factory works on a 24:"? five-shift basis. The rll cycle of operations starts at Tam (or UTUU) and ends at \"Earn the next day. This cycle is divided into 9 periods. each consisting of a two- hour' duration. For example. the rst two-hour period of the cycle lasts from UTDG to trans. The details of the breakdown of the time periods as well as the minimum number of workers required per time period are given in Table 1 below. As workers per shift are given different tasks to perform. their wages per worker varies from shift to shift. The Production Manager. together with the Human Resource Manager had worked out the cost per worker per shift. These are also given in Table 1 below. The \"E." symbols in Table 1 indicate the number of time periods that each shift of workers must work. For example= Shift 1 workers are required to work om UTDG to 151311]. (Time includes lunch of 3D minutes at 12.3pm). - - M................ \"r or kers Required u1---- nn--- un--- nnn-- -- --- --nn- ---E- ----E \"mm- Table 1: Shift vs Time period Based on the given information: (a) (b) (C) (d) State three {3) practical asstunptions applicable to this linear programming in problem. Your assumptions must be specic to the LP problem. (Assumptions = 6 marks) Develop a linear programming (LP) model to minimise the worker costs of Nano Semicon for one cycle of operations (CITES on Day 1 to UTGU on Day 2). Your model must be in the form of algebraic equations and inequalities where appropriate. Define clearly your Decision 1'"v'rariables. Objective function and Constraints. (LP model = 1? marks) Solve the LP model using the Excel Solver and present your Answer and Sensitivity Reports in their original formats generated by the Solver. (Answer Report = 3 marks} (Sensitivity Report = 3 marks) Referring to any constraint with a non-zero Shadow Price in your Sensitivity Report. explain the term \"Shadow Price\". Illustrate using an example 'om your Sensitivity Report how a non-zero Shadow Price works and state the condition(s) under which it can be applied. (Explanation = 3 marks) (lllustration of Shadow Price = 5 marks] (Condition for application = 3 marks) Due to the difculty of getting workers for Shift 5 (commonly known as the \"graveyard shift\")= the management of Nano Semicon has decided to pay more wages to attract more workers to work in that shift. As a result= the wage per worker is increased to $30. Determine the change (if any) in the objective function value due to the increase in the wage per worker for Shift 5 and obtain the new objective function solution {i.e. new Z)? (4 marks)