LaGrange Multipliers procedure says to form the quantify F* as 



F* = F - xg (D-4) 



take the total differential of equation (D-4) 



- ^ (3? ^ ^ fciTTT d(ydeh) - ... feiT^^ d(yd^hMAx) 



(D-5) 

 Rearranging 



= ^^* -(S - al) ^ ^(arydei,) - ^ afydei,)) ^(^^^h) ^ - 



^ (D-6) 



It is clear that the terms in brackets in equation (D-6) must individually 

 equal zero, however this leaves (IMAX + 2) unknown (udel i = to IMAX, A, and 

 x) and only (IMAX = 1) Equations. The (IMAX + 2)th equation is taken as 

 equation (D-3). The following system of equation then results: 



.P . IMAX JMAX ,,^ p,. 



'-^-^i - ' .'_, t-2(h .-A(y,^j-ydel.)2/3)(y.^.-ydel.)2/2] 



IMAX 



^ c AX (y. - ydel.)' 

 i=l ^ ^ ^ 



X ~'^" i AX (y. - ydel..)^/^ (D-7-1) 



103 



