Question

Bonita is testing prototype model rocket engines. To be considered a successful launch, the rocket must reach a height of at least 24 ft and must go a horizontal distance of no more than 10 ft. The vertical height must be at least three times as high as the horizontal distance. No rocket should go higher than 33 ft.

The graph shows the feasible region, where x represents the horizontal distance and y represents the vertical distance.

Which ordered pairs meet all the constraints for a successful launch and make sense in context of the situation?

Select each correct answer.



(0, 33)

(4, 36)

(4.8, 30.5)

(9, 26)

(2, 22)

Answer 1

According to the questions, Conditions are
24 ≤ y ≤ 33
x ≤ 10
y ≥ 3x

So, (0, 33) & (4.8, 30.5)

Therefore, (0, 33) & (4.8, 30.5) are the correct answers.

Answer 2

Refer to the diagram shown below.

The given constraints are
(a) y ≥ 24 ft
(b ) x ≤ 10 ft
(c) y ≥ 3x
(d) y ≤ 33 ft
The acceptable region is shown shaded.

A (0, 33) satisfies all conditions
B (4, 36) fails condition (d)
C (4.8, 30.5) satisfies all conditions
D (9, 26) fails condition (c)
E (2, 22) fails condition (a)

Answer:
The acceptable points are A and C.