Lecture 25 Ticket

Complete by the beginning of class on 11/02

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Consider the instance of the weighted knapsack problem consisting of five requests with the following durations and values:

  1. \(d_1 = 4\), \(v_1 = 3\)
  2. \(d_2 = 2\), \(v_2 = 2\)
  3. \(d_3 = 5\), \(v_3 = 5\)
  4. \(d_4 = 3\), \(v_4 = 4\)
  5. \(d_5 = 6\), \(v_5 = 5\)

Suppose your total time budget is \(B = 10\). Use the dynamic programming algorithm described in Lecture 24 to find the maximal value of a feasible collection of requests by hand. What is the collection that achieves the optimal value?

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