Question 1184905
The maximum heart rate of a person, in beats per minute, can be estimated using the expression 220 − 𝑥, where 𝑥 is the person's age in years for 20≤𝑥≤70. If it is generally recommended that at least 50% but not more than 80% of the maximum heart rate be achieved during exercise, what inequality represents the target heart rate, 𝒉, in beats per minute, over a 30-minute period years?

maximum heart rate = 220 - x, for 20 <= x <= 70.


h = the target heart rate for exercise, in beats per minute, over a 30 minute period.


your inequality will be:


h >= .50 * (220 - x)
h <= .80 * (220 - x)


this inequality can also be expressed at:


.50 * (220 - x) <= h <= .80 * (220 - x)


for a person who is 20 years old, the target heart rate during exercise is:


.50 * (220 - 20) <= h <= .80 * (220 - 20), which equals:
.50 * 200 <= h <= .80 * 200, which equals:
100 <= h <= 160.


for a person who is 70 years old, the target heart rate during exercise is:


.50 * (220 - 70) <= h <= .80 * (220 - 70), which equals:
.50 * 150 <= h <= .8 * 150, which equals:
75 <= h <= 120.


the inequality can be graphed, as shown below:


<img src = "http://theo.x10hosting.com/2021/092011.jpg" >


the opposite of the inequalities would be graphed.


inequalities for graphing are:


y <= .5 * (220 - x)
y >= .8 * (220 - x)
y <= 0
x <= 20
x >= 70


the area on the graph that is not shaded is the region of feasibility.


the coordinate points are in (x,y) format.
x represents the age of the person.
y represents the target heart rate.


for example:


a person who is 45 shows coordinates of (45,87.5) and (45,140).
(45,87.5) shows that his minimum target heart rate for exercise is 87.5
(45,140) shows that his maximum target heart rate for exercise is 140.


this is based on the inequalities of:


y >= .50 * (220 - x)
y <= .80 * (220 - x)


x is equal to 45.


y >= .50 * (220 - 45) becomes y >= .50 * 175 which becomes y >= 87.5.
y <= .80 * (220 - 45) becomes y <= .80 * 175 which becomes y <= 140.


keep in mind that the opposite of the inequalities are being graphed.
this allows the feasible region to be the unshaded region of the graph.