Consider the following data: p $8/unit Cot $9000/OT shift μ (Normal dist)) 1000/shift σ (Normal dist) 100/shift R 15 shifts (1 week) Operations are 3 shifts per day, 5 days per week. Four shifts are available during each weekend for any production “catch up” in overtime and maintenance. a) Determine the weekly profit maximizing quota. b) Determine the minimum value of M, the amount that must be produced during the weekend shifts, such that the possibility of not being able to meet the production quota ( found in part (a) ), is ≤ .02. c) At the present time, 40,000 units exist in the production line WIP and in the backlog. A new order for 1000 units has just arrived. Determine a due date quote for the new order, such that there is 95% confidence that it will be delivered within the due date lead time, measured in number of shifts. Assume no overtime (catch-up) work is done during the weekend.