- max Pv kiui u,v Σuicin Σι; Σ cout - vjaijui = 0 i=1 U1, Um 0 2 V₁, ..., Vn ≥ 0, 2
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Production planning problem:
Suppose an agency offers to extend the input and output capacities at
the factory. What are the highest prices we should be willing to pay
per unit of capacity expansion of, respectively, the input side and the
output side? Hint: If your code has a python variable someConstraint
representing a linear inequality, someConstraint.getAttr(’pi’) gives
the optimal value of the dual variable corresponding to the constraint.
Step by step
Solved in 2 steps
- After extensive planning Bonusland is constructing a road system to connect cities with in the country. The objective is to ensure connectivity between every city while minimizing expenditure on the system roads Each city offers incentive that reduces cost of connected to it. Each city i provides an incentive of t; where +; < 50, for every connecting road. These incentives have been predetermined and are recorded as [t [t....t]. Normally, constructing a road between -cities would cost exactly 100 units. However the incentives from cities i and j, the with cost is reduced to Cost (ij) = 100-t; -t; any two8. A school is creating class schedules for its students. The students submit their requested courses and then a program will be designed to find the optimal schedule for all students. The school has determined that finding the absolute best schedule cannot be solved in a reasonablo time. Instead they have decided to use a simpler algorithm that produces a good but non-optimal schedule in a more reasonable amount of time. Which principle does this decision best demonstrate? O A Unreasonable algorithms may sometimes also be undecidable O B. Heuristics can be used to solve some problems for which no reasonable algorithm exsts O C. efficiency Two algorithms that solve the same problem must also have the same O B. Approximate solutions are often identical to optimal solutionsKnapsack 0/1 problem: Given N items where each item has some weight and profit associated with it and also given a bag with capacity W, [i.e., the bag can hold at most W weight in it]. The task is to put the items into the bag such that the sum of profits associated with them is the maximum possible. Given the problem is solved using a dynamic programming approach and the matrix derived is given below, answer the below set of questions by analyzing the DP matrix. weights = [2, 3, 4, 5], profits = [1, 2, 5, 6], Capacity W = 8 Capacity 2 3 Profits weights|0 1 2 5 16 14 |-> 5 10 0 O 10 1 2 3 4 0 O 0 1 1 0 1 0 1 O 10 1 2 2 2 5 2 O 15 50 1 356 6 O 1 3 6 18 00378 7 10 10 1 3 7 7 1 18