What combination of x y and z will maximize output

Question

Problem

1. A firm buys inputs K and L at £70 a unit and £30 a unit respectively and faces the production function Q = 40K^0.5L^0.5. What is the cheapest way it can produce an output of 500 units?

2. A firm has a budget of £570 to spend on the three inputs x, y and z whose prices per unit are respectively £4, £6 and £3. What combination of x, y and z will maximize output given the production function Q = 2x^0.2y^0.3z^0.45?

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.