Suppose That the Quantity $Q$ Produced of a Certain Good Depends on the Number of Depends

question 68

Essay

Suppose that the quantity $Q$ produced of a certain good depends on the number of units of labor $L$ and the quantity of capital $K$ according to the function $Q = 900 L ^ { 1 / 3 } K ^ { 2 / 3 }$ . Suppose also that labor costs $100 per unit and that capital costs $200 per unit.(a) What combination of labor and capital should be used to produce 36,000 units of the goods at minimum cost? What is that minimum cost?
(b) Draw the level curves of $C$ , the cost function, and the graph of the constraint on the same set of axes.(c) Complete the value of $\lambda$ . What does $\lambda$ represent?