Question

Which of the points (s, t) is not one of the vertices of the shaded region of the

set of inequalities shown below?
Ss 12 -0.5t
s 10-t
SS 20-t
S20
t> 0
O A. (16,4)
B. (4,16)
O C. (0,10)
D. (0,20)

Answer 1

A (16,4)

Explanation:

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Answer 2

C. (0,10)

Explanation:

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My answer:

Given the 4 inequalities:

• s ≥ 12 - 0.5t (1)
• s ≥ 10 -t (2)
• s ≤ 20-t (3)
• s ≥ 0
• t ≥ 0

Let analyse all 4 possible answer:

• (0, 10)

Let substitute this point into (1) we have: 10 ≥ 12 -0.5*0 Wrong

We do not choose A

• (0, 20)

Let substitute this point into (1) we have: 20 ≥ 12 -0.5*0 True

Let substitute this point into (2) we have: 20 ≥ 10 - 0 True

Let substitute this point into (3) we have: 20 ≤ 20 - 0 True

We choose B as the vertex

• (4, 16)

Let substitute this point into (1) we have: 16 ≥ 12 -0.5*4 True

Let substitute this point into (2) we have: 16 ≥ 10 - 4 True

Let substitute this point into (3) we have: 16 ≤ 20 - 4 True

We choose C as the vertex

• (16,4)

Let substitute this point into (1) we have: 4 ≥ 12 -0.5*16 True

Let substitute this point into (2) we have: 4 ≥ 10 - 16 True

Let substitute this point into (3) we have: 4 ≤ 20 - 16 True

We choose B as the vertex

Hence, the point A (0,10) is not one of the vertices of the shaded region of the set of inequalities.