CASE STUDY CHALLENGE

Number Theory: Finding Factors

In number theory, it is often important to find factors of an integer N. The number N has two trivial factors, namely 1 and N. Any other factor, if it exists, is called a non-trivial factor of N.

Linear Inequations Graph

Naresh has plotted a graph of some constraints (linear inequations) with points:

  • • A(0, 50)
  • • B(20, 40)
  • • C(50, 100)
  • • D(0, 200)
  • • E(100, 0)

The graph uses three non-trivial constraints and two trivial constraints. One of the non-trivial constraints is x + 2y ≥ 100.

Answer the following:

(i) What are the two trivial constraints? [1]
(ii) (a) If R1 is the feasible region, then what are the other two non-trivial constraints?

— OR —

(b) If R2 is the feasible region, then what are the other two non-trivial constraints?

 [2]
(iii) If R1 is the feasible region, then find the maximum value of the objective function z = 5x + 2y. [1]
PreviousNext