5.15 Consider the following linear program: n maximize Pjaj j=1 n subject to j=1 j = 1, 2, ..., n j = 1, 2, ..., n.Here, the numbers p;, 7 = 1,2, ..., n are positive and sum to one. The same is true of the g;'s: > =1 =il q; > 0. Furthermore, assume that PL_P2_ _Pn q1 q2 dn and that the parameter (3 is a small positive number. Let k = min{j : ;+1+ -+ ++qn k = i=0 y; =1 0 0k See Exercise 1.3 for the motivation for this problem. (Note: The set of in- dices defining the integer & is never empty. To see this, note that for j = n1 the condition is ,,