The corner points of the feasible region determined by the following system of linear inequalities: \(2x+y\leq 10,x+3y\leq 15,x,y\geq 0\) are \((0,0),(5,0),(3,4)\) and \((0,5)\). Let \(Z=px+ay\), where \(p,a>0\) condition on \(p\) and \(a\) so that the maximum of \(Z\) occurs at both \((3,4)\) and \((0,5)\) is

\(a=3p\)

\(Z(3,4)=Z(0,5)\)