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# 1. Talcum Turnbull’s campaign has been modelling the average enthusiasm of voters for Talcum based

1. Talcum Turnbull’s campaign has been modelling the average enthusiasm of voters for Talcum based on the number of emails and phone calls they receive from the campaign. In one area of the electorate the campaign ﬁnds that enthusiasm is approximated by f(x,y) = 10 + 3y−y2 −2ex −xy where x is the number of emails received and y is the number of calls received. (a) Find ∇f(x,y). [2] (b) In this area, the campaign has been operating on a “2 emails, 2 calls” strategy. They are only prepared to make a slight adjustment to this (one more or one fewer email or one more or one fewer call). What would you advise? (Use your answer to (a) to guess the best adjustment, and then check that this adjustment is an improvement.) [3]
2. Shill Borton’s campaign ﬁnds that voter enthusiasm in his electorate is approximated by g(x,y) = 6x + 4y + xy−x2 −2y2

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