Consider a firm which produces according to the following production function by using labor and capital:

$f(k,l)=k^{\frac{1}{4}}|\frac{1}{2}|$

a$.$ Solve the cost minimization problem of this firm for the given wage rate, $w$ and the rental rate of capital, v$.$

b$.$ Derive the cost function of the firm.

c$.$ Decide whether the production function exhibits constant, increasing or decreasing returns to scale.