Problem $3$:

Crozet Cozy Chairs $($CCC$,$ Inc.$)$ produces three kinds of hand crafted outdoor, ultra$-$lightweight,

totally hip chairs: sling chairs, Adirondack chairs and hammocks. The unit profit for each of these

products is $$35\mathrm{.}00,$$$75\mathrm{.}00$ and $$100,$ respectively. Each type of chair requires cutting, assembly,

and finishing time. The owner is retired, but she is willing to work $120$ hours per month. She does

not want to work more than $50$ hours per month doing any one of the specific activities, cutting,

assembly or finishing. These chairs are very popular in Crozet, so as usual she can sell all she

makes. Sling chairs require $30$ minutes for cutting, assembly requires $45$ minutes, and finishing

takes $1$ hour. Adirondack chairs take $2$ hours for both cutting and assembly and $1$ hour for

finishing. The very popular hammock model requires $24$ minutes for cutting, $3$ hours to assemble,

and $1$ hour to finish. How many of each chair should the owner make to maximize profit? $($hint:

sum the time to produce each chair type, use the values as coefficients for a constraint. Be careful

with units... need all be the same$)$