A manufacturing process for a widget has four stages and involves $4$ parts. In Section A parts $1$ and $2$ are assembled. In Section B parts $3$ and $4$ are assembled. In Section C the two assemblies are welded together and finally in Section D the widget is painted and packaged. Sections A and B have $5$ assembly machines each. Each assembly machine in Section A has an output of $50$ parts per hour and each machine in section B has an output of $60$ parts per hour. Section C has $8$ welding machines each of which has an output of $40$ parts per hour and Section D has $6$ painting machines each of which has an output of $75$ parts per hour. All machines need one worker each to operate. Purchase costs of the parts are follows: