U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5

As a mathematical function, does U have a maximum or minimumvalue? What values of Ci correspond to the minimum value of U? Whatvalues of Ci correspond to the maximum value of U? Do these valuesof Ci make sense from an economic standpoint?

Now let us connect the idea of economic utility to actual dollarvalues. To keep the values more manageable, we will use householdincome rather than the entire state budget, and retail costs andmeasures rather than industrial ones. Find the Median HouseholdIncome for Mesa, AZ for the most recent year possible. Then findthe dollar cost in Mesa, AZ for a Penny, a pound of Ground Beef, apair of Jeans, fresh Orange Juice, and a Movie Ticket.(Entertainment is often used as a stand-in for Climate.) A Cost-of-Living Index is a good place to find much of this data. Recordthese prices as P1, P2, P3, P4, and P5 respectively.

Construct an equation using Median Income, the Ci and Pi valuesthat illustrates how much of each resource the Median Household canafford to purchase. Given this restriction, do the maximum orminimum values of U change? Do the values of Ci that give themaximum or minimum values change? What are these new values? Howshould the Median Household budget its Income so as to maximize itsEconomic Utility?

Write up your findings in a paper that you could turn in to anemployer. Be sure to show all your work. Include any appropriatereferences as well as any computational devices used.

* Solve the questions, make the table, and thegraph.