Write down the firms cost minimization problem

Question

Problem: Consider a firm with production function f(z₁, z₂) = 4z₁^0.5 + 3z₂^0.5

(1) Sketch the isoquant diagram of this firm.

(2) Derive the marginal rate of technical substitution between the two inputs. What is the relationship between the marginal rate of technical substitution and the isoqants drawn in subquestion (1).

(3) Does the function f exhibit decreasing, constant, or increasing returns to scale? Is f homogenous of some degree k>0?

(4) Write down the firm’s cost minimization problem.