Consider that you are working for a delivery service, where you can go to the warehouse and pick items to deliver. each item i has a cost and weight ci, as well as the address to where to deliver. you have a limit w on how much weight your van can carry. for every item you deliver, you earn 10% of its cost you are also provided with a map of the town with all the possible of addresses of the items in the warehouse, and the distances between them. every mile you travel costs you $1. for simplicity you can consider the items are packaged and cannot be divided further. also there is a direct path between all pairs of addresses, although the distances may differ. each address receives exactly one item. 1. develop an algorithm, where given the list of items, their weights, costs and delivery ad- dresses, you can select the items to pick for 1trip, that brings you maximum profit. clearly explain the algorithm in english (stepl, ) and demonstrate how it works for an example problem (20+20=40) 2. implement the algorithm and try it on 5 different set of inputs. each input consists of a list of items and a complete graph of addresses, along with their distance. there should be at least 200 items on the list and 200 addresses. submit your code and your results (20+20=40)

For each of the following claims, determine whether they are true or false. justify your determination (show your work). if the claim is false, state the correct asymptotic relationship as o, θ, or ω. unless otherwise specified, lg is log2.(a) (b) (c) (d) (e) (f) (g) (h) (i) (j)n+1 =22n =2n =1 =ln2 n =n2 +2n−4 =33n = 2n+1 =√n = 10100 =o(n4) o(2n)θ(2n+7 ) o(1/n)θ(lg2 n) ω(n2 )θ(9n ) θ(2n lg n )o(lg n) θ(1)

Write a computer program to calculate the three-phase fault current for a fault at f in figure 1.16, with the network normal, and with one line at a time removedproblems 1.1 write a computer program to calculate the three-phase fault current for a fault at f in figure 1.16, with the network normal, and with one line at a time removed 20 power system relaying from service. the positive-sequence impedance data are given in the accompanying table. use the commonly made assumption that all prefault resistance values are (1.0+j0.0) pu, and neglect all resistance values. calculate the contribution to the fault flowing through the cb b and the voltage at that bus. for each calculated case, consider the two possibilities: cb b2 closed or open. the latter is known as the stub-end fault í• figure 1.16 problem 1.1 system data for figure 1.16 from to positive sequence 0.0+j0.1 0.05j0.15 0.04 j0.2 0.01 jo.i 0.015 + j0.15 0.01 j0.19 0.01 +j0.19 0.03+j0.1 0.0+j0.08 6 6 6 from service. the positive-sequence impedance data are given in the accompanying table. use the commonly made assumption that all prefault resistance values are (1.0 + j 0.0) pu, and neglect all resistance values. calculate the contribution to the fault flowing through the cb b1, and the voltage at that bus. for each calculated case, consider the two possibilities: cb b2 closed or open. the latter is known as the “stub-end” fault.

Under which key category do the page up and page down keys fall? page up and page down keys fall under the keys category.