4 points = 1+ 1 + 1 + 1 points) IP problem. The owner of a machine shop is planning to expand by purchasing some new machinespresses and lathes. The owner has estimated that each press purchased will increase profit by $100 per day and each lathe will increase profit by $150 daily. The number of machines the owner can purchase is limited by the cost of the machines and the available floor space in the shop. The machine purchase prices and space requirements are as follows.

3. (4 points = 1+1+1+1 points) IP problem. The owner of a machine shop is planning to expand by purchasing some new machines presses and lathes. The owner has estimated that each press purchased will increase profit by $100 per day and each lathe will increase profit by $150 daily. The number of machines the owner can purchase is limited by the cost of the machines and the available floor space in the shop. The machine purchase prices and space requirements are as follows. Required Machine Floor Space (ft) Purchase Price Press Lathe 15 30 $8,000 4,000 The owner has a budget of $40,000 for purchasing machines and 200 square feet of available floor space. The owner wants to know how many of each type of machine to purchase to maximize the daily increase in profit. a) Formulate an integer programming problem and make the decision variables are restricted to integer values b) Convert the above problem- a) it as binary integer programming (BIP). c) If you know the incumbent solution currently is (2,5) and Z*=950. At one B&B step/subproblem (A), the solution of its LP relaxation is (3, 4), are there any fathoming tests satisfied/passed (i.e., stop division)? If yes, by which criterium, Test 1, 2, or 3? Will you update the incumber solution value? d) If you know the incumbent solution currently is (2,5) and Z*=950. At one B&B step/subproblem (B), the solution of its LP relaxation is (1.33, 6) and Z = 1033.33, are there any fathoming tests satisfied/passed (i.e., stop division)? If yes, why? If no, how will you branch it as two subproblems