After pre-qualifying a number of suppliers, ARC created a shortlist of two potential suppliers (S1 & 52), and now they need to make a decision on which supplier(s) to choose and how many panels they order from each. ARC's objective is to minimize total cost, LT, and quality (measured by reject rates). The fixed costs to place an order for any product to the two suppliers are $1500 and $2000, respectively. The demand for each type of LCD panel is 2000 and 3000 per year, respectively. Detailed quantitative data on the two suppliers are provided in the tables below. 

a) Formulate this supplier order allocation problem with the three objectives as a MILP in an OPEN FORM using the parameter values given above. Use % value for quality (e.g. use 8, not 0.08 for the first row in the table). DO NOT define redundant or unnecessary variables and indices in your model; doing so will be penalized. Please number all the equations/inequalities in your model ((1), (2), ...) as we need to reuse them in part b). 

b) Modify the MILP model developed in part a) into a Preemptive Goal Programming model with the three conflicting goals (cost > LT > quality, in the order of importance). You can reuse the equations/inequalities you defined in part a) by referring to the corresponding equation numbers. If you modify, say equation (1), re-number it as (1)'.

Product Supplier 1 1 1 2 2 1 2 2 Capacity 1800 2400 2800 3000 Price/Unit 120 150 160 200 LT 15 16 17 18 Quality (%) 8 6 7 5