SOLUTION: A manufacturer of cell phones makes a profit of $25 on a deluxe model and $30 on a standard model.The company wishes to produce at least $80 deluxe models and at least 100 standard

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Question 250495: A manufacturer of cell phones makes a profit of $25 on a deluxe model and $30 on a standard model.The company wishes to produce at least $80 deluxe models and at least 100 standards model per day. To maintain high quality , the daily production should not exceed 200 phones. How many of each type should be produced daily in order to maximize the profit?
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
First we have a profit function as:
P+=+25D+%2B+30S
Second, we have D >= 80 and S >= 100. graph those on a coordinate system where D is x-axis and S is y-axis.
Third, we have D + S <= 200. Graph that on a coordinate system. Notice we get a "feasible region" which looks like a small triangle. We want the coordinates of the three verticies. They are: (80, 100) ; (80,120) ; (100,100).
Put these into the profit function and we get,
P+=+25%2A80+%2B+30%2A100 - -> P = 5000
P+=+25%2A80+%2B+30%2A120 - -> P = 5600
P+=+25%2A100+%2B+30%2A100 - -> P = 5500.
WE can see max profit at (80, 120).
we need to produce 80 deluxe and 120 standard.