Instant Pot produces a popular multicooker appliance called the Duo. The Duo is produced in a factory that operates 24 hours per day (in 3 shifts of 8 hours), 365 days per year. The final product consists of the pot/control panel assembly and one lid. The net profit on each Duo, after considering all relevant costs, is $20 per unit. You can assume that demand for the Duo is so strong that Instant Pot can sell as many Duo devices as they can produce. The production process that Instant Pot uses to manufacture the Duo consists of five steps: Pot Production: It takes 1 person 10 minutes to manufacture a pot. There are 8 people working on pot production during each shift Lid Production: An injection molding machine produces lids in batches of 25. The machine can produce one batch every 20 minutes, and is operated at all times. Control Panel Production: It takes one person 4 minutes to produce a control panel, and there are 4 people working on control panel production during each shift. Duo Assembly: During assembly, the pot and control panel of the Duo are integrated. Each shift has 4 people working on Duo assembly, and it takes 1 person 6 minutes to assemble a Duo. Duo Test: Each Duo that is produced is tested on Instant Pot's single test machine. The machine tests the Duos in batches of 15. It takes 9 minutes to set up the machine, and then 12 seconds to test each Duo. 95% of Duos pass inspection. When a Duo fails inspection, the pot/control panel assembly is sent to another division of Instant Pot for recycling (i.e., neither the pot nor the control panel can be used to make a Duo). The only reason a Duo fails inspection is due to a defect in the control panel. Lids are not impacted by the test process. (a) (20 points) How much profit does the factory generate in a day? (b) (15 points) Instant Pot is considering the possibility of adding a second model, called the Lux, which will be a higher end version of the Duo. The Lux has a more advanced control panel, which will take 1 person at the control panel production step 6 minutes to produce. The Lux will also be packaged with two lids (in case one is dirty or breaks). All other facets of production of the Lux are identical to the Duo, and all work on the Lux will use the company's existing resources. Instant Pot earns a profit of $30 on each Lux it sells. Assuming that an equal number of Duo and Lux pots will be produced and sold, what is the daily profit after adding the Lux to the product line? (c) (10 points) Instant Pot is considering the purchase of a new type of testing machine. The machine costs $350,000 and has the following two features: (1) it does not require any set up as it does not test in batches (but it still takes 12 seconds to test a control panel). (ii) it does not have to wait until the control panel has been assembled with the pot, i.e., it can test control panels earlier in the process. Assuming Instant Pot still produces an equal mix of their Duo and Lux pots, will the new testing machine pay for itself within one year? Please justify your answer. (Note: assume for simplicity that there is no disposal cost/value associated with retiring the current machine.)