4. Setting up an LP from a practical problem. In the fine tradition of bad puns on mathematical assignments, my colleagues and I are starting the soon-to-be-famous Opple Rubber Company. Our company makes three different products: . fashionable rubberised slippers sold under the "iMoc" name . rubberised protectors for fruit called "oPods", and . a small annoying musical instrument called the "oPhone". Our company receives the rubber it needs in 200em long ribbons. Each product requires a certain amount of rubber. . 1 pair of iMoc slippers needs 90cm of a ribbon . 1 oPod needs 70cm of a ribbon . 1 oPhone needs 50cm of ribbon A large order has come in and the company needs to make at least . 300 pairs of iMocs . 400 oPods . 1000 oPhones We would like to work out how to cut up the sheets so as to minimise waste. This problem can be broken down into smaller parts: (a) 2 marks | There are 6 ways to cut a 200cm rubber sheet into pieces of length 90cm, 70cm and 50 cm with minimal waste - what are they and how much rubber does each one waste? Please list them in order of most waste to least. Note Do not include ways such as (70, 70) since this leaves 60cm and one could cut a 50cm segment from it. (b) 4 marks | Each of the ways of cutting a sheet wastes a certain amount of rubber. Obviously we would like to minimise this waste while still producing enough iMocs, oPods and oPhones. For some reason our cutting machine is unable to cut the ribbon in four equal pieces, so ignore this possibility - this leaves the other five cutting options. Write this as a linear programming problem. You have to explain your answer. Note Please label your variables v1, ...,/'s so that the corresponding amount ribbon wasted is ordered from greatest to least. (c) 4 marks Write and run a Jupyter notebook to solve the LP problem from (b). You must attach the screenshot of your Jupyter notebook and results (d) 5 marks | Write down the dual problem to the problem of (b). Then write and run a Jupyter notebook to solve it. You must attach the screenshot of your Jupyter note- book and results. Also check whether the optimal objective value of this problem is the same as the optimal objective value of the problem in (b)