$(25$ points$)$ You are given $n$ jobs numbered $1,2,$dots,$n$ and each job comes with a difficulty $d_i.$

Each job takes exactly one week to complete irrespective of its difficulty. If you complete job

i during week $j(n),$ then you earn a profit of $d_i(n-j).$ Your objective is to maximize

the sum of the profit. Consider a greedy strategy that completes the jobs in the decreasing

order of difficulty. Prove$/$disprove that such a strategy produces an optimal solution.