NVidia, the pioneering computer graphics chip maker has a line of production of a semiconductor component of one of its chips. The production process represents number of units produced per day (Q) as a function of labor (L), which costs $400 per unit, and capital (K), which costs $800 per unit. The following production function describes the process:

Q=3L(^2) K

Elasticity of the production function with respect to labor and capital are:

Marginal product of capital and marginal product of labor are:

Average product of labor and average product of capital are:

If labor is currently fixed at L=6, what is the short-run production function

If capital is currently fixed at K=4, what is the short-run production function?

If the goal of the firm is to produce 48,000 units a day, the optimum combination of K and L required at this level of production is: