Question: The linear production function is

\[Q=F\left( K,L \right)=aK+bL\]

where K is equal to capital and L is equal to labor. The Cobb-Douglas production function is

\[Q=F\left( K,L \right)={{K}^{1/2}}{{L}^{1/2}}\]

A firm produces output (hamburgers or whatever) that can be sold at $10.00. Production function is the Cobb Douglass formula above if capital is fixed at 1.

How much labor should the firm employ to maximize profits if the wage rate is $2.00

Hint: Set the value marginal product of labor equal to the wage rate and solve for L. Value marginal product of labor is

\[VM{{P}_{L}}=P\times M{{P}_{L}}\]