Solve by graphical method:

$($a$)$ A bald cypress, which would sell for $$50,$ needs

$5$ gallons of water and $10$ grams of fertilizer

each week. A live oak, which would sell for $$80,$

needs $2$ gallons of water and $3$ grams of fertil$-$

izer each week. Each week there are $90$ gallons

of water and $150$ grams of fertilizer available.

If a local plant nursery wants to maximize their

revenues while having at least two bald cypress

trees available, how many of each type of tree

should they grow? Discuss leftovers.

$($b$)$ A large clay pot requires $85$ units of clay and

$5$ labor$-$hours to produce. A small decorative

clay pot requires $14$ units of clay and $11$ labor$-$

hours to produce. Due to warehouse space, no

more than $622$ large clay pots and no more than

$950$ small clay pots can be produced. There

are only $12,250$ labor$-$hours and $61,200$ units of

clay available. If the profit for a large clay pot

is $$32$ and a small clay pot is $$5,$ how many

of each type should be produced and sold to

maximize profit? Discuss leftovers.

$($c$)$ An ice sculpturer creates carvings of dolphins

and mermaids. For a dolphin, it takes $5$ hours

to freeze the water and $3$ hours to carve. For

a mermaid, it takes $2$ hours to freeze the wa$-$

ter and $4$ hours to carve. Each week there are