WeProtect is a small family business that breathes new life into household objects, giving them a professional clean followed by an application of a protective layer of varnish. Each process (cleaning or varnishing) can only be applied to one object at a time, although both processes can be carried out simultaneously on different objects. On one particular day, WeProtect has four objects that need to be cleaned and then varnished: a chair, a bookcase, a mirror frame and a table. These objects need to be prepared in the shortest possible overall time. The times in minutes required for each process on each object are as follows: Process Object Chair Bookcase Mirror frame Table Cleaning 20 35 20 25 Varnishing 10 15 8 12 (a) Assuming that these are the only objects to be treated that day, formulate WeProtect's problem as an integer programming problem. (b) Which object should be varnished last in order to obtain an optimal solution? Explain your answer. (c) Based on your answer to (b), determine an optimal solution for the problem, giving the values of all the variables introduced in (a) and their meanings in terms of the original problem. [8] [3] WeProtect is a small family business that breathes new life into household objects, giving them a professional clean followed by an application of a protective layer of varnish. Each process (cleaning or varnishing) can only be applied to one object at a time, although both processes can be carried out simultaneously on different objects. On one particular day, WeProtect has four objects that need to be cleaned and then varnished: a chair, a bookcase, a mirror frame and a table. These objects need to be prepared in the shortest possible overall time. The times in minutes required for each process on each object are as follows: Process Object Chair Bookcase Mirror frame Table Cleaning 20 35 20 25 Varnishing 10 15 8 12 (a) Assuming that these are the only objects to be treated that day, formulate WeProtect's problem as an integer programming problem. (b) Which object should be varnished last in order to obtain an optimal solution? Explain your answer. (c) Based on your answer to (b), determine an optimal solution for the problem, giving the values of all the variables introduced in (a) and their meanings in terms of the original problem. [8] [3]