What amounts of the inputs x y and z should a firm use

Question

Problem

1. What amounts of the inputs x, y and z should a firm use to maximize output if it faces the production function Q = 2x^0.4y^0.2z^0.6 and it has a budget of £600, given that the prices of x, y and z are respectively £4, £1 and £2 per unit?

2. A firm buys the inputs x, y and z for £5, £10 and £2 respectively per unit. If its production function is Q = 60x^0.2y^0.4z^0.5 how much can it produce for an outlay of £8,250?

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.