What combination of k and l firm use to maximize output

Question

Problem

1. Make up your own constrained optimization problem for an objective function with two independent variables and solve it using the substitution method.

2. A firm faces the production function Q = 2K^0.2L^0.6 and can buy L at £240 a unit and K at £4 a unit.

(a) If it has a budget of £16,000 what combination of K and L should it use to maximize output?

(b) If it is given a target output of 40 units of Q what combination of K and L should it use to minimize the cost of this output?

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.