What combination of l and k firm use to maximize production

Question

Problem

1. If a firm has a budget of £378 what combination of K and L will maximize output given the production function Q = 40K^0.6L^0.3 and prices for K and L of £20 per unit and £6 per unit respectively?

2. A firm faces the production function Q = 6K^0.4L^0.5. If it can buy input K at £32 a unit and input L at £8 a unit, what combination of L and K should it use to maximize production if it is constrained by a fixed budget of £36,000?

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.