$2$ O$.$J$.$ Juice Company sells bags of oranges and cartons

of prange juice. O$.$J$.$ grades oranges on a scale of $1($poor$)$

$1010($excellent$).$ O$.$J$.$ now has on hand $100,000lb$ of grade

$9$ oranges and $120,000lb$ of grade $6$ oratiges The average

quatity of oranges sold in bags must be at least $7,$ and the

average quality of the oranges used to produe orange juice or

must be at least $8.$ Each pound of oranges that is used for

juice yichds a revenue of $$1\mathrm{.}50$ and incurs a variable cost

$($consisting of labor costs, variable overhead costs, inventory

costs, and so on$)$ of $$1\mathrm{.}05.$ Each pound of oranges sold in

bags yields a revenue of $50c$ and incurs a variable cost of

Formulate an LP to help O$.$J$.$ maximize profit.