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Math 211 Math for Business Analysis
Project #4
Another line on the 5 C’s
In the first Project we optimized “economic utility” for a household based on an economy comprised entirely of the Five C’s (Cattle, Citrus, Climate, Copper, and Cotton). That model of economic utility showed a very tight interdependence of the various sectors, because as a product the lack of even resource made the other four valueless. At the other extreme would be an economy where the value of each sector was completely independent of the rest. One such Utility Function could be:
U(C1, C2, C3, C4, C5) = C1+C2+C3+C4+C5
Where, as before, the Ci represent the number of economic units purchased: lbs., gal., etc.
While this function could be optimized using the same methods as the first Project, the fact that it is linear makes it a candidate for Linear Programming. (Many times economic models are assumed to be linear not because they are the most accurate, but because they are the most “tractable”, or easy to solve.) But to do that we will need many more restrictions on the values.
Use the Prices and Median Household Income you found for the first Project to create a budget restriction. In addition, use the following limitations:
The combined amount of Orange Juice and Ground Beef must be at least one thousand units.
The number of Movie Tickets must not exceed two hundred.
The number of Pennies must be no more than one thousand.
The number of pairs of Jeans must be between a minimum of fifty and a maximum of two-hundred and fifty.
First, translate all the restrictions into a system of inequalities.
Second, use the system of inequalities and the equation for economic Utility, as well as any necessary Slack or Surplus variables to construct a Linear Programming tableau.
Then use row operations to move the tableau into the “feasible space”. (In other words, no negative solutions.)
Finally, solve the tableau, and explain what the results mean in terms of the Five C’s.
(If you use any calculator functions, computer programs, or web apps, please be sure to list them.)