Zak$$s trading card company is deciding much cardboard $($k$)$ and labor $($l$)$ it needs to e$$iciency produce collectable trading cards. Given that Zak has $10,000$ to spend on l and k$,$ and pl $=10$ and pk $=5.$ If the production of trading cards uses the production function f $($l$,$ k$)=$ l $14$ k $34,$ find the optimal quantities of l and k$.$

$1)$ Set up the Lagrangian $2)$ Find $$L$,$L$,$L

$3)$ Solve for $\backslash$lambda

$4)$ Solve for k

$5)$ Plug into the budget constraint and solve for l$,$k$$