$1)$ Solve the following problem using iso$-$profit lines or level curves.

Min $2$x$1+3$x$2$

S$.$t$.$

$2$x$1+$ x$23$

$4$x$1+5$x$220$

$2$x$1+8$x$216$

$5$x$1+6$x$260$

x$1,$ x$20$

$(1)$ has a production capacity of $40,000$ lbs$.$ each quarter with a per unit cost of $$400$ per thousand lbs using regular labor,

$(2)$may have workers work overtime where the per unit cost increases to $$450$ per thousand lbs$.,$

$(3)$ incurs a holding cost of $$20$ per thousand lbs$.$ at the end of a period.

How many lbs$.$ of paint should PCBCo produce to satisfy demand while minimizing total production and inventory costs? $($Hint: The inventory cost is based on the amount stored at the end of the period!$)$