Ron$$s Chair Shop is a small shop in Pawnee, Indiana, that produces three types of chairs: models A$,$

B$,$ and C$.$ Each chair requires a certain amount of time for cutting, assembling, and then staining.

Ron also sells unstained versions of each model. The times $($in hours$)$ for each phase of construction,

the profit margins for each model, as well as the amount of labor hours available in each department

over the next week are given in the table below.

Ron$$s chairs are of such high quality that he can easily sell every unit that his shop produces. Also,

Ron knows that he will need at least $20$ model B chairs $($either stained or unstained$)$ over the next

week, and in order to increase the sale of stained chairs, Ron wants to produce at most $50$ unstained

chairs over the next week. Formulate a linear program whose solution would tell Ron what his shop

should produce in order to maximize profits over the next week.