Question

Daniel works at least 28 hours a week. He works as a math tutor
and as a teacher. The number of hours Daniel works as a tutor (y) is at least twice
the number he works as a teacher (x).
Write the set of inequalities that represents the constraints of the situation
and state a point (x, y) that is the feasible region.

Answer 1

Here, we are required to rite the set of inequalities that represents the constraints of the situation and state a point (x, y) that is the feasible region.

• The set of inequalities that represents the constraints of the situation are; y + x ≥ 28 and y ≥ 2x

• A point (x, y) that is the feasible region is therefore; (x ≥ 9.33, x ≥ 9.33)

• According to the question; Daniel works at least 28 hours a week. This means he can work more but not less.
• i.e. y + x ≥ 28

The number of hours he works as a tutor, (y) is at least twice the number he works as a teacher (x).

The inequality for the expression above is therefore;

y ≥ 2x

By substituting y = 2x for y into equation;

y + x ≥ 28

we have 2x + x ≥ 28

x ≥ (28/3)

x ≥ 9.33

Also, y is at least twice of x.

y ≥ 9.33 × 2

Therefore, y ≥ 18.66

A point (x, y) that is the feasible region is therefore;

(x ≥ 9.33, x ≥ 9.33)

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