Your company creates software using $4$ computer programmers. You can employ them in whatever numbers you wish either to write code, W$,$ or test code, T$.$ You$$ve examined various combinations of programmer allocations between W and T and the results for the average completed software application per programmer$$call it the average product, AP$$are shown in the following table.

$1.$ The optimal allocation of your $4$ programmers is $($x$)$ for W and $($x$)$ for T which yield a total of $($xx$)$ programs.

$2.$ Assuming you pay $$100$ to each programmer and programs sell for $$100$ each your profits are $ $($xxxx$).$