A Company Produces Three Products Which Must Be Painted, Assembled

Essay

A company produces three products which must be painted, assembled, and inspected. The machinery must be cleaned and adjusted before each batch is produced. They want to maximize their profits for the amount of operating time they have. The unit profit and setup cost per batch are:
$\begin{array}{ccc}\text { Product } & \text { Profit per unit } & \text { Setup cost per batch } \\\hline 1 & 9 & 500 \\2 & 10 & 600 \\3 & 12 & 650\end{array}$
The operation time per unit and total operating hours available are:
$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\underline{\text {Operating Time per Unit}}$$\quad$$\quad$$\quad$$\quad$$\quad$$\text {Operating}$
$\begin{array}{lcccc}\text { Operation } & \text { Product 1 } & \text { Product 2 } & \text { Product 3 } & \text { Hours Available } \\\hline \text { Paint } & 1 & 2 & 2 & 400 \\\text { Assemble } & 2 & 3 & 2 & 600 \\\text { Inspection } & 2 & 4 & 3 & 540\end{array}$
Formulate the ILP for this problem.