B23 .: X fi B 14 Problem 5 Suppose you are a business analyst working for Company 1, and the main competitor of your company is Company 2 which produces two machines, A and B. You find 10 groups of data of monthly total profit, production numbers of Machine A and B of your rival from the internet, as is showed in "Problem 5 of the given excel table. Suppose that the profit of Company 2 only comes from the sales of Machines A and B and that in every month all machines are sold. In addition, there is a monthly maintenance cost of the manufacturing factory, which has be subtracted in the profit showed in the data. In other words, Total profit = Profit of Machine A + Profit of Machine B - Maintenance fee Your target is to estimate the (unknown) monthly maintenance fee and the unit profits of Machine A and B of your rival from their data. In addition, you know that the monthly maintenance fee is at least $15K from your experience. 1) Formulate the optimization problem of least square linear regression to estimate the three parameters, namely, the maintenance fee and the unit profits of Machines A & B. (15 points) Hint: Consider the "total profit as y, the maintenance fee and the unit profits of Machines A & B as Bo, B1 and B2, respectively. Be careful that maintenance fee = -Bo (why?). Then, based on the 10 data, you can build a regression model (see page 18 of Lecture 1) to fit these three parameters (i.e., Bo,B1 and B2). Do not forget the constraint Bo