A team of economists recently worked with resource managers in Santa Fe to find out what measures could be taken to draw more visitors to our state parks in order that scarce budgets could better serve visitors. After much study, they found that visits produced (V) from a State Park is approximately predicted by: (1) V = 20000 L 0.10 S 0.40 where L is the hours of staff hired and S is the number of campsites installed. The total cost (TC) of managing the park is: (2) TC = 20 L + 10000 S i.e. each added hour of staff is priced at $20 and each added campsite installed is priced at $10,000, and the total cost depends on how many of L and S are hired, both unknown (endogenous) in advance. Suppose total gross benefits (TGB) to park visitors are defined as a constant benefit of $10 per visit multiplied by the V defined by the equation above, i.e. TGB = 10V. Total net benefit (TNB) produced by the parks is calculated as total gross benefits (TGB) minus total costs (TC) of management described above, i.e. TNB = 10 V(.) - TC(.), where the mathematical functions for V(.) and TC(.) are defined above. a. Derive the first order necessary conditions (FONC) for the two variable inputs employed that maximize TNB, where there is no constraint on the total budget. Show work for all parts. b. How many staff hours and campsites hired maximizes total net benefits? c. How many visits are produced by your optimized hiring decision? d. What is the total budget cost per year of those purchased inputs? e. What value of TNB is achieved by your optimal hiring decision? 2. Suppose that budget cuts by the legislature limit the NM State Parks budget to $1 million/year. a. Reformulate the problem as a constrained maximization using the method of LaGrange multipliers. Show work for all parts. b. Derive the first order conditions for constrained maximum of TNB, consisting of 3 equations in 3 unknowns (L,S, ). c. Solve those three equations for the optimal values of the 3 variables: (L*,S*,*). d. Provide an economic interpretation for the optimal values of staff and campsites. e. What loss in total visitation is produced by the $1 million upper bound on budget in problem 2 compared to the unconstrained optimized budget in problem 1. f. Interpret the calculated value of your Lagrangian multiplier so that a legislator can understand.