Following the example in the text, consider two HIV prevention programs: (1) intensive counseling of high-risk individuals and
(2) instituting a needle-exchange program for intravenous drug users. Counseling has an estimated cost of $1,500 per individual per year and is expected to prevent .2 new HIV cases per individual helped. The needle- exchange program costs $500 per individual and prevents .1 new HIV cases per individual.

a. Which program is more effective at HIV prevention per individual treated? Which program is more cost effective, that is, more effective per dollar spent? Do your answers raise a dilemma as to which program to fund?

b. Suppose that a regional health organization has a total budget of
$450,000 to spend on the two programs and has identified 1,000 high-risk individuals. In coordinating the two prevention programs, it sets two variables, C and N, for the respective numbers to be counseled or furnished clean needles. (Given their very different orientations, the programs are mutually exclusive; each individual is enrolled in a single program.) If the authority's goal is to prevent as many new HIV cases as possible, how many individuals should it enroll in each program?

c. What is the authority's optimal allocation if the at-risk population numbers only 250? Show that it will have unused funds.

d. Finally, what is the authority's optimal allocation if the at-risk population numbers 500? Be sure to show the appropriate LP formulation.