Consider the production function $Q=K+2L^{\frac{1}{2}}$ with $w=1$ and $r=10.$

$a.$ Plot the isoquant for $Q=10.$

$b.$ Write down the long$-$run cost minimization problem for $Q=10.$

$c.$ Demonstrate that the solution $isat$ a corner point.

$d.$ Derive the condition $onr$ for $an$ interior solution

$e.$ Suppose the solution $is$ interior. Derive the cost$-$minimizing $L$ and $K.$ Determine $ifL$ and $K$ are normal inputs.

$f.$ Suppose the solution $is$ interior. Calculate the elasticity $of$ labor demand with respect $tow.$