3. MHD Selection & Assignment Model A manufacturer produces three part types. Their production sequences and annual production volumes are given as follows: P1: M1-M4-M3; 10,000 units/year P2: M4-M2-M3; 8,000 units/year P3: M1-M4-M2-M3; 12,000 units/year The manufacturer considers two types of MHDs to transport the items between machines: H1 and H2. The purchasing cost per unit is $100,000 and $140,000, respectively. Using the unit transportation cost (and time [min]) data given in the table below, we need to determine the required number of each of the two MHDs and assign them to the various moves. M2 M3 M4 10 (6) 6 (14) 8 (2) 6 (15) 18 (6) 12 (14) From To M1 P1 M1 H1 H2 M4 H1 H2 P2 M4 HI H2 M2 H1 H2 P3 M1 IN H2 M4 HI H2 M2 HI H2 12 (6) 6 (12) 6 (8) 8 (6) 8 (6) 7 (9) - 14 (12) 12 (16) Formulate the problem as a mathematical model in OPEN form. You don't need to solve it to obtain the optimal solution. Assume the length of planning period - 50 wks/yr * 5 days/wk * 2 shifts/ day * 8 hrs/shift 60 min/hr = 240,000 minutes and 100% effective time for the MHDs