Difficult inequality story problem.. Please help by Superbowl Sunday night!

Ok, Im in finite math and this homework problem has me all confused. I cant seem to find the last inequality to graph. Here is the problem.

Mostpure milk company buys milk from two local dairies and then blends the milk to get the desired amount of butterfat for the companys premier product. Milk from Dairy A costs $2.40 per gallon and milk from Dairy B costs 0.80 per gallon. At most $144 is budgeted for purchasing milk. Dairy A can supply at most 50 gallons of milk averaging %3.7 percent butterfat and Dairy B can supply at most 80 gallons of milk averaging 3.2% butterfat. How much milk from each supplier should Mostpure use to get at most 100 gallons of milk with the maximum amount of butterfat.

So far i have these inequalities:
2.40x + 0.80y < 144
x < 50
y < 80

Im not sure what i need to complete this problem and graph the solution region. Please help i have to turn it in early monday morning! Thanks a bunch (Hi)

Hello, kylezj!

Quote:

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Mostpure Milk Company buys milk from two local dairies
and then blends the milk to get the desired amount of butterfat.
Milk from Dairy A costs $2.40 per gallon and milk from Dairy B costs 0.80 per gallon.
At most $144 is budgeted for purchasing milk.
Dairy A can supply at most 50 gallons of milk averaging 3.7% butterfat
and Dairy B can supply at most 80 gallons of milk averaging 3.2% butterfat.

How much milk from each supplier should Mostpure use to get at most 100 gallons
of milk with the maximum amount of butterfat?


So far i have these inequalities: . . . . . Good!

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They want a total of 100 gallons (at most): .

. . And we must maximize: .