Question

Assume that the approval rating of a Prime Minister is given by the function Ad, e), where d is defence spending (in billions) and e is education spending in billions). The output of the approval rating Ad, e) itself is a percentage between 0 and 100. It is desirable to predict how changes to defence and education spending impact upon the PM's approval. With current spending at do and eo, the rate that approval (in percentage) changes with respect to defence spending in billions) is measured by Newspoll to be the partial derivative ando,eo) = 6.9, so an increase in defence spending of 1 billion dollars will translate to an increase in approval of 6.9%. Similarly the rate that approval changes with respect to education spending is measured to be the partial derivative (do,0) = 5.7. Hence by the total differential approximation, for [d, e] in the neighbourhood of [do, eol A(d, e) – A(do, eo) + dà (do, eo)(d – do) + JA (do, eo)(e – eo). The current approval rating is Ado, eo) = 52. If defence spending is decreased by 1 billion and education spending increased by 0.2 billion, then the approval rating approximately changes to Number Note: do not round your answer, approval rating is too important to be rounded.

Answer 1

Given A(d, e) z Aldo, eo) + JA (do, eo) (d-do) + JA (do,eo) (eco) JA (do, eo)=619, JA (do,eo) = 5.7 да current approver rating Aldo,eo) 252 defenco spending decreased by I billion d-do=1 Educating spending Increased by 0.2 billion. e-co=012 Acd, e)=52+ (619)(-1) + (517) (012) =52+(-6:9)+ (1.14) = 52-619 +1114 = 46.24 A(d, e) = 46.24 Approval rating es 46.24%