SOLUTION: As a receptionist for a veterinarian, Sue schedules appointments. She allots 20 minutes for a routine office visit and 40 minutes for a surgery. The vet cannot do more than 6 sur

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Question 168678: As a receptionist for a veterinarian, Sue schedules appointments. She allots 20 minutes for a routine office visit and 40 minutes for a surgery. The vet cannot do more than 6 surgeries per day. The office has 7 hours available for appointments. If the office visits cost $55 and most surgeries cost $125, how many office visits and surgeries should Sue schedule to maximize the veterinarian's profit/
I am not sure how to set up the constratints and graph.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
She allots 20 minutes for a routine office visit and 40 minutes for a surgery. The vet cannot do more than 6 surgeries per day. The office has 7 hours available for appointments. If the office visits cost $55 and most surgeries cost $125, how many office visits and surgeries should Sue schedule to maximize the veterinarian's profit/
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I am not sure how to set up the constraints and graph.
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Let x = no. of office visits
Let y = no. of surgeries
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"Cannot do more than 6 surgeries a day
y =< 6; a red horizontal line
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Let's deal in minutes here: 7 hrs = 420 min
20x + 40y =< 420
Rearrange equation for graphing purposes
40y =< 420 - 20x
y =< 10.5 - .5x; green line
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graph these two equations, shade the area at or below the lowest line:
+graph%28+300%2C+200%2C+-6%2C+25%2C+-5%2C+16%2C+6%2C+10.5-.5x%29+
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The three corners of this area: x=0, y=6; x=9, y=6; x=21, y=0
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Profit equation:
P = 55x + 125y
Calculate the profit using each coordinate
55(0) + 125(6) = $750
55(9)+ 125(6) = $1245
55(21)+ 125(0) = $1155
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We can can max profit is when they have 9 office visits and 6 surgeries.
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Check to make sure we obey the time constraint
20(9) + 40(6) = 420 min, exactly the time available
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How about this? Did it make sense to you?