Question

A doctor allots 15 minutes for routine office visits and 45 minutes for full physicals. the doctor cannot

do more than 10 physicals per day. the doctor has 9 available hours for appointments each day. a
routine office visit costs $60 and a full physical costs $100. how many routine office visits and full
physicals should the doctor schedule to maximize her income for the day? what is the maximum
income?

Answer 1

1 full physical and 33 routine visits per day to maximize income for the day.

Maximum income is $2080.

Explanation:

The doctor has 9 hours per day which equals to 9 x 60 = 540 minutes

If there are 10 physicals per day, the maximum minutes will be 45 x 10 = 450 minutes.

so the time left for routine office visits will be 540 - 450 = 90 minutes

then the number of routine office visits will be 90 / 15 = 6

Her income will be ($100 x 10) + ($60 x 6) = 1000 + 360 = $1360

If there is 1 physical per day, then the time will be 45 x 1 = 45 minutes

so time left for routine office visits will be 540 - 45 = 495 minutes

then the number of routine office visits will be 495 / 15 = 33

Her income will be ($100 x 1) + ($60 x 33) = 100 + 1980 = $2080

If there are 2 physicals per day, then the time will be 45 x 2 = 90 minutes

so time left for routine office visits will be 540 - 90 = 450 minutes

then the number of routine office visits will be 450 / 15 = 30

Her income will be ($100 x 2) + ($60 x 30) = 200 + 1800 = $2000

Answer 2

• 36 routine visits
• 0 physicals

Explanation:

You want to maximize the doctor's income when she makes $60 for a 15-minute routine visit and $100 for a 45-minute physical. She can work 9 hours per day.

Earning rate

For a routine visit, the doctor is charging $60 for 15 minutes, or $4 per minute.

For a physical, the doctor is charging $100 for 45 minutes, or $2.22 per minute.

Clearly, the doctor earns income faster by spending her time doing routine office visits. There appears to be no limit on the number of those she can do.

Working 9 hours at $4 per minute, the doctor earns ...

(9 h/day)(60 min/h)($4/min) = $2160/day

Appointments

The number of routine visits in a day will be ...

(9 h/day)(60 min/h)/(15 min/visit) = (9·60/15) visits/day = 36 visits/day

The doctor's maximum income is $2160 per day, making 36 routine office visits per day.

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Additional comment

Each physical will reduce the doctor's income by $80. (In that 45 minutes, she could have done 3 routine visits, for a revenue of 3·60 = 180, instead of the physical for a revenue of 100.)