A manufacturing company produces several semi$-$finished products $($A$,$ B$,$ C and

D$)$ that are integrated in the final products. Due to the high customization

requirements, it is not possible to keep the semi$-$finished goods on stock, which

means that the demanded parts have to be produced every week. To do so$,$ four

machines are available and each machine is dedicated to exactly one product.

The machines are generally available for $40$ hours per week because they require

labour to be run. Each additional hour on one of the machines $($overtime$)$ costs

$40$