A manufacturer produces two products, the Sly and Robby. The Sly has a contribution of $5$ per unit and the Robby $6$ per unit. The manufacturer wishes to establish the weekly production plan which maximises contribution.$$

Production data are as follows:$$

$-----$per unit$-----$

Machine hours Labour hours Material $($kg$)$

Sly $542$

Robbie $362$

Total available per week $12018080$

Due to a trade agreement, sales of Sly are limited to a weekly maximum of $15$ units and to honour an agreement to an old established customer at least $12$ units of Robby must be produced per week.$$

Using the following notation:

z $=$ contribution

x $=$ the number of Sly$$s

y $=$ the number of Robby$$s

When plotting points on a graph for the material constraint, the points which intersects with both the x and y axis are: