Consider the following constrained maximization problem:

maximize y $14$x$15$lnx$2$ subjectto kx$1$x$2140,$

where k is a constant that can be assigned any specific value.

Showthatifk$1410,$thisproblemcanbesolvedasoneinvolvingonlyequalityconstraints.

Show that solving this problem for k $144$ requires that x$1141.$

Ifthex$$sinthisproblemmustbenonnegative$,$whatistheoptimalsolutionwhenk$144?$

What is the solution for this problem when k $1420?$ What do you conclude by comparing this solution to the solution for part $($a$)?$