Consider a hospital that produces output (Q) and has two production inputs, nurse-hours (N) and beds

(B). the hospital faces input costs of W_N = 15 and W_B = 25. Assume the hospital's production function is: Q =N^αB^1-α, where α^1/2.

a) If the hospital's desired output level is Q = 120, find B∗ and N∗ that minimize cost.

b) What is the hospital's total cost, C, of producing this level of output using B∗ and N∗?

c) Suppose the state government imposes a certificate of need constraint on the number of beds. The new CON rule limits the number of beds to B_R = 250. Assuming the hospital would like to keep its output level at 120, how many nurse-hours (N_R) will it require?

d) Suppose instead the CON rule limits the number of beds to B_R ′ = 100. Again, assuming the hospital keeps its output level constant, how many nurse-hours (N_R′) will it now require?

e) What is the hospital's total cost of producing this level of output using B_R′ and N_R′?

f) Now suppose the hospital must keep its costs equal to its costs before the CON law. How many nurse-hours will it now require? What will its new output level be?