The Donaldson Furniture Company produces three types of rocking chairs: the children's model, the standard model, and the executive model. Each chair is made in three stages: cutting, construction, and finishing.

The time needed for each stage of each chair is given in the chart. During a specific week the company has avallable a maximum of $162$ hours for cutting, $102$ hours for construction, and $80$ hours for finishing. Determine how many of each type of chair the company should make to be operating at full capacity.

$\backslash$table$[[$Stage$,$Children's,Standard,Executive$],[$Cutting$,5hr,4hr,7hr$