Draw the Network for This Assignment Problem

question 38

Essay

Draw the network for this assignment problem.
$$\begin{array} { l l } \text { Min } & 10 x _ { 1 A } + 12 x _ { 1 B } + 15 x _ { 1 C } + 25 x _ { 1 D } + 11 x _ { 2 A } + 14 x _ { 2 B } + 19 x _ { 2 C } + 32 x _ { 2 D } \\& + 18 x _ { 3 A } + 21 x _ { 3 B } + 23 x _ { 3 C } + 29 x _ { 3 D } + 15 x _ { 4 A } + 20 x _ { 4 B } + 26 x _ { 4 C } + 28 x _ { 4 D } \\\text { s.t. } & x _ { 1 A } + x _ { 1 B } + x _ { 1 C } + x _ { 1 D } = 1 \\& x _ { 2 A } + x _ { 2 B } + x _ { 2 C } + x _ { 2 D } = 1 \\& x _ { 3 A } + x _ { 3 B } + x _ { 3 C } + x _ { 3 D } = 1 \\& x _ { 4 A } + x _ { 4 B } + x _ { 4 C } + x _ { 4 D } = 1 \\& x _ { 1 A } + x _ { 2 A } + x _ { 3 A } + x _ { 4 A } = 1 \\& x _ { 1 B } + x _ { 2 B } + x _ { 3 B } + x _ { 4 B } = 1 \\& x _ { 1 C } + x _ { 2 C } + x _ { 3 } C + x _ { 4 C } = 1 \\& x _ { 1 D } + x _ { 2 D } + x _ { 3 D } + x _ { 4 D } = 1\end{array}$$

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Definitions:

Direct Labor

The wages and other costs for labor that is directly involved in the production of goods or services.

Fixed Overhead

Regular, unchanging costs that a business incurs, regardless of the level of production or sales activity, such as rent and salaries.

Direct Labor

The work of employees that can be directly attributed to the production of goods or services.

Fixed Overhead

Regular, fixed expenses associated with the operations of a business that do not vary with production volume.