By A.G. Buckley, J-.L. Goffin
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Extra resources for Algorithms for Constrained Minimization of Smooth Nonlinear Functions
6. The first step to take in this problem is to identify the variables of interest. There are five variables, Which can be defined as follows: Let X let C let D letS and let 0' be be be be be the the the the the number of debits made during the year, number of cheques made during the year, number of direct debits made during the year, number of standing orders made during the year, proportion of debits made during the year which are cheques. (i) This part of the problem requires us to find a relationship between 0' and X.
4) Rearrange ( 4) by adding 44 to both sides to give, I OP + 4P = 12 + 44 14P =56 P=P0 =56/14=4 To find the value of Q0 , substitute the value of P0 into (3) togiveQ 0 =22-2x4= 14 METHOD 2 - ELIMINATION First, let Qd = Qs = Q, Then we have, 2P + Q = 22 ... (1) 10P-2Q=l2 ... (2) We can eliminate Q by multiplying ( 1) by 2 and adding the resulting equation to (2), so we have 4P+ 2Q = 44 ... (3) lOP- 2Q = 12 ... (2) which on adding gives, 14P =56 P=P0 =56/l4=4 To find the value of Q0 , substitute the value of P 0 into (1) to give 2 x 4 + Q0 = 22 Q0 = 22 - 2 x 4 = 14 The set of equations given above are called CONSISTENT since there exists a unique solution.
_ [ ______1:". e. the slope, of the function f(x). e. the curvature, of the function f'(x). Hence, the second derivative gives us information about both the magnitude of the change in f'(x) and the direction of the change in f'(x), as x changes by very small amounts. g. 14 Economic Concepts Since Total Revenue (TR) is a function of the level of output (Q), we can defme Marginal Revenue (MR) as the alteration in the value of total revenue brought about by a small change in the amount of the good sold.
Algorithms for Constrained Minimization of Smooth Nonlinear Functions by A.G. Buckley, J-.L. Goffin