urgent $!!!(50$ points$)$ The research department $of$ a manufacturing company arrived $at$ the following

Cobb Douglas production function for a particular product:

$N(x,y)=10x^{0\mathrm{.}6}{y}^{0\mathrm{.}4}$

$In$ this equation, $xis$ the number $of$ units $of$ labor and $yis$ the number $of$ units $of$ capital

required $to$ produce $N(x,y)$ units $of$ the product. Each unit $of$ labor costs $$30$ and each unit

$of$ capital costs $$60.$

$If$ $$300,000is$ budgeted for production $of$ the product, determine how that amount should

$be$ allocated $to$ maximize production, and find the maximum production. $(Hint$: Use Lagrange

Multipliers$)$