Linear programming, Algebra 2 Honors

Question

a doctor allots 15 minutes for routine office visit and 45 minutes for for physicals. The doctor cannot do more than 10 physicals per day. The doctor has nine available hours for appointments each day. A routine office visit costs $60 and a full physical costs $100. how many routine office visit and for physicals should the doctor schedule to maximize her income for the day?

Answer 1

So, there are a few ways to look at this problem. Let's start by defining the unknowns:

 

Number of Physicals, P (≤ 10)

Number of Office Visits, V

 

two variables require two equations to solve.

Let's start by writing an equation for money $$$ made per day:

 

M = 60V + 100P

 

Now an equation for time. (in hours)

 

9 = 0.25V + 0.75P

 

This second equation should be re-written for substitution.

 

0.25V = 9 - 0.75P

 

V = 36 - 3P

 

Substitute (36 - 3P) in for V in the second equation.

 

M = 60(36 - 3P) + 100P

 

M = 2160 - 180P + 100P

 

M = 2160 - 80P

 

From here you can probably see that the fewer Physicals the more money because there's that -80P . In fact, the best scenario would be zero physicals. 9hrs/0.25hrs = 36 office visits would bring in the most money.

 

You could also compare the rate for each;

Physicals 100$/0.75hr = 133.33 dollars per hour 

Office Visits 60$/0.25hr = 240 dollars per hour

you can see that the hourly rate for physical is almost half that of the office visits.

 

Best scenario ; 0 physicals, 36 office visits