Suppose production function, Y = (2L(3/4))(4K(1/4)). Cost function, C = wL+rK (where w=wage rate & r=cost of capital).
i) Using Lagrangian method, find the Least Cost of production. First, define the Objective function and Constraint. Second, find the solution for optimal units of labour and capital, L* and K*. Note: during solution, do not use values given in (ii)
ii) If w = $5/hr; capital cost, r = $10/hr, what is the cost of producing Y = 200.
iii) For the same problem, find the optimal units of Labour (L*) and Capital (K*) that will maximize Profit.