It is often said that the economy of Arizona depends on the “Five C’s”: Copper, Cattle, Cotton, Citrus, and Climate. Assume a (highly simplified) model of the Arizona Economy that depends only on C1, C2, C3, C4, and C5, which represent the number of economic units (pennies, pounds, etc) purchased of each of the Five C’s, respectively. Further assume that the Utility, or Economic Value (which is different from Dollar Value), can be described by the function: U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5 As a mathematical function, does U have a maximum or minimum value? What values of Ci correspond to the minimum value of U? What values of Ci correspond to the maximum value of U? Do these values of Ci make sense from an economic standpoint?
Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
It is often said that the economy of Arizona depends on the “Five C’s”: Copper, Cattle, Cotton, Citrus, and
Climate. Assume a (highly simplified) model of the Arizona Economy that depends only on C1, C2, C3, C4,
and C5, which represent the number of economic units (pennies, pounds, etc) purchased of each of the Five
C’s, respectively. Further assume that the Utility, or Economic Value (which is different from Dollar
Value), can be described by the function:
U(C1, C2, C3, C4, C5) = C1∙C2∙C3∙C4∙C5
As a mathematical function, does U have a maximum or minimum value? What values of Ci correspond to
the minimum value of U? What values of Ci correspond to the maximum value of U? Do these values of Ci
make sense from an economic standpoint?
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