Consider a firm with a production function 𝑞 = √𝑧, and it uses only one input (for example labour) to pr

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Consider a firm with a production function 𝑞 = √𝑧, and it uses
only one input (for example labour) to produce q units of output.
The price of every unit of input is w and the price of every unit
of output is p (note that w>0 and p>0).
(a) Write the firm’s profit maximization problem and solve for
its unconditional factor demand.
(b)Using the demand for z obtained in (a), find the level of
output q.
(c) Set up the firm’s cost minimisation problem and solve for
its conditional factor demand for any level of output level q.