A Cement Company Has Three Factories That They Identify as Alpha

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?