A manufacturing firm is designing supply chain network and has selected three potential sites, Delhi, Mumbai, and Chennai to serve markets of Kolkata, Bengaluru, Hyderabad, and Nagpur. The firm estimates cost of building plant, production, transportation, and tax rate for each manufacturing location which are shown below: Kolkata Bengaluru Hyderabad Nagpur Capacity Plant cost Production cost/unit Tax rate Delhi 140 220 270 130 500 80,000 4.00 31% Mumbai 270 127 250 261 590 100,000 3.50 29% Chennai 185 120 133 169 520 70,000 4.25 25% Demand 360 390 400 340 (a) Build an optimization model. (b) If all costs except transportation cost are ignored, find out number of units that a plant should supply to certain market(s), such that the firm incurs minimum cost. (c) If all costs are considered, how should the firm meet different market demands from their existing manufacturing plants such that their total cost of meeting demands should be minimum. (d) Instead of building three plants of different capacity as shown in the above Table, a plan under discussion is if they build high (800 unit) or low (500 unit) capacity plant, will they be able to meet the demand in a more cost-effective fashion? To build low and high capacity plant, the firm estimates a cost of 70,000 and 95,000 respectively. (e) From the part (d), if demand of Nagpur increases by 10% every year, when supply chain network will be required to be revamped and how?