Make up your own constrained optimization problem

Question

Problem

1. Inputs K, L, R and M cost £10, £6, £15 and £3 respectively per unit. What is the cheapest way of producing an output of 900 units if a firm operates with the production function Q = 20K^0.4L^0.3R^0.2M^0.25?

2. Make up your own constrained optimization problem for an objective function with three variables and solve it.

3. A firm faces the production function Q = 50K^0.5L^0.2R^0.25 and is required to produce an output level of 1,913 units. What is the cheapest way of doing this if the per-unit costs of inputs K, L and R are £80, £24 and £45 respectively?

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.