3) Ocean Internet Cables DG-Lynx is a manufacturer of "ocean Internet cables" 1 (submarine communication cables). For the production plan of the next quarter, the company is considering two types of cable. The manufacturing department is required to produce the following amounts by the end of each month of the plan (demand table below): Demanded cable lengths (in kilometers). Plant availability (hours). Date Plant-1 Plant-2 [30 marks] Date Type-A Type-B Jan 31 8,000 2,000 Feb 28 16,000 10,000 Mar 31 Total 6,000 10,000 Feb Mar Jan 1,400 3,000 600 2,000 800 600 30,000 22,000 Note that the entire demand must be fulfilled, and the cables are shipped to customers at the end of the month based on the above demand table. The excess production of the month enters inventory at the end of that month. That is, during the month while the cables are being produced, no inventory cost incurs. Two plants can be allocated for the production of these orders. The number of hours available and the time it takes to produce one kilometer of each type of cable are given in the plant availability table above and the production rate table below, respectively: The costs involved in the plan are as follows ( is a fictitious currency used in this problem): A kilometer of either cable costs 10.00 per hour to produce at either plant. Plant production rates (hours per kilometer). Date Plant-1 Plant-2 Type-A Type-B 0.30 0.32 0.24 0.28 There is a holding (inventory) cost of 2 0.20 per kilometer of either cable per month. The raw material cost is 2 6.20 per kilometer of Type-A and 27.80 per kilometer of Type-B. The packing cost is 20.46 per kilometer of either type. The selling price is ? 14.00 per kilometer of Type-A and 2 18.00 per kilometer of Type-B. Formulate and solve a mathematical program (MILP) to answer the following questions: 1. Devise a production schedule for the maximum possible total profit (revenue minus costs), while meeting all requirements. 2. How much is the total profit under the optimal production schedule you have devised? Hint: There should be no inventory at the end of March, i.e., the demanded lengths of each month must be fulfilled by the end of each month, and the production in January and February may carry over inventory to the next month (on top of fulfilling the demand of the month). Because of the very long distance to satellite orbits (35,000 km above Earth), which notably delays the transmission and reception of signals (data), over 95% of the global Internet traffic goes through oceans (https://www.submarinecablemap.com). One of the longest such submarine links (2Africa) is 45,000 km, ranging from the UK to India, while surrounding Africa. It connects several countries on its path. Not only are satellite distances too long, but they also have to be traversed twice for each transmission (or reception)-once to the satellite from the origin and once from the satellite to the destination-making it effectively twice as long (70,000 km).