Question 1166360
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As a receptionist for a hospital, one of Elizabeth's tasks is to schedule appointments. 
She allots 60 minutes for the first visit and 30 minutes for a follow-up. 
The doctor cannot perform more than eight follow-ups per day. 
The hospital has eight hours (480 minutes) available for appointments. 
The first visit costs $120 and the follow-up costs $70. 
Let x be the number of first visits and y be the number of follow-ups. 
Write a system of inequalities to represent the number of first visits and the number of follow-ups 
that can be performed.

What is the maximum income that the doctor receives per day? 
a. $960 b. $1,040
c. $970 d. $1,920

Determine the number of first visits and follow-ups to be scheduled to make the maximum income.
 a. 16 first visits and 0 follow-ups b. 4 first visits and 7 follow-ups
c. 8 first visits and 0 follow-ups d. 4 first visits and 8 follow-ups
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        If the goal is to solve the minimax problem and to find the maximum income (with learning something useful on the way),

        then the problem can be solved  MENTALLY  without writing any equations and/or any inequalities,

        and without making trial-and-error calculations.



<pre>
From the problem, two follow-ups visits require 30+30 = 60 minutes and provide the income 
of $70+$70 = $140. It is greater than one first visit, which requires the same time of 60 minutes
and provides the income of $120.


Therefore, the idea is to schedule as many pairs of 30 minutes follow-ups visits as it is possible
under the problem's restrictions, and then to fill the rest of the time by 60-minutes first visits.


Since the doctor has the restriction to serve no more than 8 follow-ups visitors per day,
it IDEALLY fits to this scheme: 

    8 follow-ups visits PLUS 4 first time visits,

giving the maximum possible income of  8*70 + 4*120 = 1040 dollars per day and satisfying all restrictions.
</pre>

Solved.



In my view,  this way solving/reasoning is MUCH better than to follow the instructions in the post.


Why ? - - - Because it teaches to think and to see the solution via thinking, instead of 
simply follow instructions and making trials-and-errors, as if a person/(a student) is mentally blind.