A Cement Company Has Three Factories That They Identify as Alpha

question 5

Essay

A cement company has three factories that they identify as Alpha, Beta, and Gamma. They supply cement to three warehouses referred to as X, Y, and Z. The company wants to determine how much cement should be shipped from each factory to each warehouse to minimize shipping costs. The cost to ship each 100-pound bag, along with warehouse requirements and factory capacities in bags are shown in the table below:
$\begin{array}{lccccc}&&\text { Warehouses }\\\text { Factories }&X&Y&Z&\text { Capacities (bags) }\\\text { Alpha } & \$ .40 & \$ .60 & \$ .78 & 10,000 \\\text { Beta } & 0.65 & 0.78 & 0.59 & 9,000 \\\text { Gamma } & 0.56 & 0.61 & 0.71 & 7,000 \\\text { Requirements (bags) } & 10,000 & 5,000 & 10,000 &\end{array}$
a. How many decision variables are there in this problem?
b. What is (are) the constraint(s) corresponding to factory Alpha?
c. How many constraints are required for this problem?

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Definitions:

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A specific marker found on the surface of certain blood cells, contributing to blood type differentiation in the ABO blood group system.

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A default hypothesis that there is no statistical significance in a set of given observations, essentially stating that any observed effect is due to chance.

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