In many different social networks ,each person prefers to meet with people from their own community and are reluctant to switch affiliations. If they switch, they pay a penalty for switching csw and if they visit a meeting of a community different from their own they pay a penalty for visiting cvis . Suppose all the meeting rooms have different colors representing communities. Let there be T time steps 1, …, T , n people 1, …, n, and R rooms. Then let a matrix of observed meetings of people in those times be Mij , where mij ⊆ {1, …, n} is the set of people (which may be empty) that met at time i in room j. For example, the matrix that describes the observations in figure 4.1 is M = [ {1; 2; 3} {4} {5} {1; 3} {2; 4} {5} {1; 3} {4} {2; 5} {1; 3} {4} {2; 5} {1; 3; 4} {2; 5} ] Given the M matrix and the penalties csw and cvis , give a dynamic programming algorithm that assigns a community color to each individual at each time step so that the total sum of all the penalty costs incurred by all the individuals is minimized. You can use the fact that the each person’s contribution to the overall minimum is independent. Prove that fact.

 

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In many states, political power is concentrated in the hands of few wealthy elites. Imagine you belong to a group that is losing its traditional freedom or quality of life due to government policies but feel that your political representatives are unwilling or unable to defend your interests. Would you challenge the state authorities or accept your degenerating condition without public protest? Why or why not?

 

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In march 2014 andrew thorne acquired a four unit apartment building at a cost of $875,000. Of this total, it is estimated that the land on which the building is situated is worth $185,000. The units in the apartment are similar in size and for purposes of allocation to a CCA class, the property is considered to be a single asset.

Two of the units will be rented on a furnished basis. To this end, Andrew has acquired furniture at a cost of $43,000.

During April 2014, all of the units were rented for the remainder of the year. For this year, the units generated rents of $63,600 and expenses, other than CCA, of $23,400 were incurred.

In July 2015, the tenants in both of the furnished units terminate their leases, and move out. Because he is unable to find tenants who are interested in furnished units, the two units remain empty for three months. Given this situation, Andrew sells all of the furniture for $31,000.

During 2015, the units generate rents f $54,500. Expenses for the year, other than CCA, total $29,400.

Andrew deducts the maximum CCA allowable in both 2014 and 2015.

Required: Calculate the Net Rental income for each of the two years 2014 and 2015. Also, determine his UCC balances on January 1, 2016. Include in your solution and tax consequences associated with the sale of the furniture.

 

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In March, a derivatives dealer offers you the following quotes for June British pound option contracts (expressed in U.S. dollars per GBP):Market price of contractcontract/strike price/bid/offercall/USD 1.40/0.0642/0.0647put/0/0.0255/0.0260call/USD 1.44/0.0417/0.0422put/0/0.0422/0.0427call/USD 1.48/0.0255/0.0260put/0/0.0642/0.0647Assuming each of these contracts specifies the delivery of GBP 31,250 and expires in exactly three months, complete a table similar to the following (expressed in dollars) for a portfolio consisting of the following positions:(1)long one 1.44 call(2)short one 1.48 call(3) long one 1.40 put(4) short one 1.44 putJune USD/GBP1.361.401.441.481.52

 

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In March, volunteers for a charity walkathon in Toronto raised $89,351. Volunteers in Montreal raised $102,459. Volunteers in Edmonton raised $78,505. a. Round each amount to the nearest thousand dollars.b. Add the rounded amounts to estimate the total amount of money raised.c. Use the estimate to choose the exact total from among the following.

 

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