Problem $32.$ Budgeting for maximum production. A manufacturing firm has budgeted $$60,000$ per month for labor and materials. If $$x$ thousand is spent on labor and $$y$ thousand is spent on materials, and if the monthly output $($in units$)$ is given by

$N(x,y)=4xy-8x$

then how should the $$60,000$ be allocated to labor and materials in order to maximize $N?$ What is the maximum $N?$