Mathematics

Problem

For the system of inequalities

x - y \ge 2

y \ge 1

x \ge 0

, consider the expression

S = 4x + y

to be maximised. a. (i) Draw the feasible region determined by the constraints. b. (ii) Determine whether

S

attains a finite maximum value in the feasible region. Give a clear justification based on your graph. c. (iii) Find the minimum value of

S

, if it exists, and the corresponding point.