friends and family to visit in Los Angeles (5,200 miles roundtrip), Miami
(2,520 miles), and Durham, North Carolina (1,224 miles)—all of which
have American direct flights from Boston. (Each roundtrip counts as two
flight segments.)
a. She is ready to book her trips, and the cheapest American roundtrip
fares to the three cities are $425, $300, and $200, respectively. How
should she plan her numbers of trips to these destinations to meet the
mile and segment challenge at minimum total cost? Using a
spreadsheet and optimizer, formulate and solve her linear program.
(In the optimizer menu, be sure to include the constraint that the
number of trips to each destination must be an integer.)
b. How would her trip plan and total cost change if 25,000 flown miles were
required? What if only 10 segments (and 20,000 miles) were needed?Discussion Question 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.Spreadsheet Problems
S1. An electronics firm has production plants in Oregon and Tennessee. It
ships its products overseas from three ports: Los Angeles, New Orleans,
and New York. Transportation costs between plants and seaports are
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