2. (a) Pineapple Inc. are commissioning three production lines to produce a new [10] type of laptop. They will produce at least 190,000 laptops. For each line: the line will be switched on if and only if it will produce at least 20% of its capacity; the commissioning cost, production cost per laptop, and capacity are as in Table 1 (all costs are in S$) Line Commiss. cost Prod. cost/laptop Capacity 3,800,000 175 150,000 B 3,200,000 180 100,000 1,800,000 190 80,000 Table 1: Pineapple laptop production: costs in S$ and capacities. Formulate mathematically the problem of minimising total production cost, briefly explaining each part of your work. (6) Explain why complete enumeration is not a practical approach to solving [15] large IP problems. Describe how Branch and Bound attempts to overcome the issues with complete enumeration. In your answer, cover pruning poli- cies and explain the terms bounding function, incumbent and fathoming. 3. (a) Figure 1 shows a small social network G. Showing the details of your work, [15] find the degree, closeness and betweenness centrality measures for the actor labelled as 4. 2. (a) Pineapple Inc. are commissioning three production lines to produce a new [10] type of laptop. They will produce at least 190,000 laptops. For each line: the line will be switched on if and only if it will produce at least 20% of its capacity; the commissioning cost, production cost per laptop, and capacity are as in Table 1 (all costs are in S$) Line Commiss. cost Prod. cost/laptop Capacity 3,800,000 175 150,000 B 3,200,000 180 100,000 1,800,000 190 80,000 Table 1: Pineapple laptop production: costs in S$ and capacities. Formulate mathematically the problem of minimising total production cost, briefly explaining each part of your work. (6) Explain why complete enumeration is not a practical approach to solving [15] large IP problems. Describe how Branch and Bound attempts to overcome the issues with complete enumeration. In your answer, cover pruning poli- cies and explain the terms bounding function, incumbent and fathoming. 3. (a) Figure 1 shows a small social network G. Showing the details of your work, [15] find the degree, closeness and betweenness centrality measures for the actor labelled as 4