Macro q1 thank you

A representative rm which only can survive for one period. It has the following technology: Y = zF(K, N ), where K is the given capital stock (the representative rm owns K but no market value if the rm sells it), N is labor demand by paying competitive market wage rate to, and z is total factor productivity (TFP). Let's further assume the production function be a continuous concave function. Without loss of generality, let's assume the output good price equals to 1. (a) Write down the representative rm's prot function and graphically determine and mathe- matically prove the prot maximization coudition. (8 marks) (b) Determine the labor demand curve, N, as a function of wage, 1:). Graph this relationship. (6 marks) (0) Suppose that the pandemic improves technology due to the improving remote work-from-home technology that save a lot of commute time. La, 2 increases. Discuss and graph the change of labor demand curve. (8 marks)