The firms has the production function Q(K,L)=30K^.67L^.33, where Q is the hours of edited footage. The wage is $25, and the rental rate of capital is $50. The firm wants to produce 3,000 units of output (video shorts) at the lowest possible cost.
a. What ratio of capital to labor minimizes cost?
b. How much capital and labor will you need to rent and hire in order to produce 3,000 units of output?
c. What is the total cost of hiring these inputs?
d. Graph the isocost and isoquant associated with this example. Clearly mark the optimal point. Include the quantity and cost on the isoquant and isocost.