Consider the system of linear inequalities
x−2y≤4,x+y≥3,x≥0,y≥0.
Let P=5x+3y be an objective expression.
a. (i) Draw the feasible region for the given constraints on a suitably chosen scale.
b. (ii) From your graph, state whether the feasible region is bounded or unbounded. Give a short reason based on the geometry of the region.
c. (iii) Examine the behaviour of P in the feasible region and decide whether it attains a finite maximum value. Justify your answer with reference to the graph obtained in part (i).