Summary 749Suggested References
The following reference is one of many fine, applied programming texts.
Gass, S. I..An Illustrated Guide to Linear Programming. New York: McGraw-Hill, 1990.
The following articles describe typical managerial applications.
Kaplan, E. “Allocating HIV Resources.” OR/MS Today(February 2001): 26–29. The panel’s full
report is available online at: http://www.nationalacademies.org (search for “No Time to Lose” full text).
The direct link is http://www.nap.edu/books/0309071372/html/
Higle, J. L., and S. W. Wallace. “Sensitivity Analysis and Uncertainty in Linear Programming.” Inter-
faces(July–August 2003): 53–60.
Bollapragada, S., et al. “NBC’s Optimization Systems Increase Revenues and Productivity.” Interfaces
(January–February 2002): 47–60.
LeBlanc, L. J. et al. “Nu-kote’s Spreadsheet Linear Programming Models for Optimizing Trans-
portation.” Interfaces(March–April 2004): 139–146.
Kimes, S. E., and J. A. Fitzsimmons. “Selecting Profitable Sites at La Quinta Motor Inns.” Interfaces
(March–April 1990): 12–20.
Linear programming software is surveyed by
Fourer, R. “Linear Programming: Software Survey.” OR/MS Today(June 2011): 60–69, also available
online at http://www.lionhrtpub.com/orms/surveys/LP/LP-survey.html.CHECK STATION
ANSWERS- The formulation of the farmer’s problem is
where W and B denote the amounts (in thousands of bushels) of wheat
and barley, respectively. Graphing the problem reveals that both
constraints are binding. Solving simultaneously the equations W B
10 and 4W 2B 32, we find W 6 thousand bushels and B 4
thousand bushels. The resulting revenue is $13,600.- As long as PW/PBis between 1 and 2, the crop mix W 6 and B 4 is
optimal. (For instance, a 15 percent fall in both prices has no effect on
the ratio.) A rise in the price of wheat to $2.25 puts the ratio outside this
range, causing the farmer to produce only wheat. The new solution is W
8 and B 0, with only the labor constraint binding. A fall in the price of
wheat to $.90 causes the farmer to produce only barley. Now the solution
is B 10 and W 0. - To find the shadow price of land, solve the equations W B 11 and
4W 2B 32 to arrive at W 5 thousand bushels and B 6 thousand
bushels. The farmer’s new revenue is $14,000. Land’s shadow price is the
difference between the old and new revenues, $14,000 $13,600 $400.
To find the shadow price of labor, solve the equations W B 10 and
4W 2B 33 to arrive at W 6.5 and B 3.5. Labor’s shadow price is
4W2B 32 1 labor 2 ,
Subject to: WB 10 1 land 2
Maximize: R1.6W1.0B
c17LinearProgramming.qxd 9/26/11 11:05 AM Page 749