A neighborhood health clinic has a budget of $600,000per quarter. The director of the
Chapter 15, Problem 34(choose chapter or problem)
A neighborhood health clinic has a budget of $600,000per quarter. The director of the clinic wants to allocatethe budget to maximize the number of patient visits, V ,which is given as a function of the number of doctors, D,and the number of nurses, N, byV = 1000D0.6N0.3.A doctor gets $40,000 per quarter; nurses get $10,000per quarter.(a) Set up the directors constrained optimization problem.(b) Describe, in words, the conditions which must besatisfied by V /D and V /N for V to have anoptimum value.(c) Solve the problem formulated in part (a).(d) Find the value of the Lagrange multiplier and interpretits meaning in this problem.(e) At the optimum point, what is the marginal cost of apatient visit (that is, the cost of an additional visit)?Will that marginal cost rise or fall with the numberof visits? Why?
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