1. Profit maximization

Find and that maximizes the following profit function.

(,)=5022242+6056.

2. Profit maximization for perfectly competitive firm

A firm produces output using two inputs capital and labor

using the production function

=12^1/2^1/3

Assume output price=2 per unit,rent=3 per unitand wage=4 per unit.

Find the profit maximizing input levels and and also the maximum profit.