Consider the unconstrained NLP

max x$1$x$25($x$12)43($x$25)4$

$($a$)$ Use a graphing software to produce a contour map of the objective function for

x$1"[1,4],$ x$2"[2,8].$

$($b$)$ Compute the move direction that would be pursued by gradient ascent algorithm

at x$(0)=(1,3).$

$($c$)$ State the line search problem implied by your direction.

$($d$)$ Solve your line search problem graphically and compute the next search point

x$(1).$

$($e$)$ Do two additional iterations of the gradient ascent to compute x$(2)$ and x$(3).$

$($f$)$ Plot progress of the search on the contour map of part $($a$).$