Let x kg of B1 and y kg of B2 are taken for making brick.
Here, Z = 5x + 8y is the cost which is objective function and is to be maximised subjected to following constraints.
x + y = 5 ….. (i)
x ≤ 4 …..(ii)
y ≥ 2 ........(iii)
x ≥ 0, y ≥ 0 ….. (iv)
In this case, constraint (i) is a line passing through the feasible region determined by constraints (ii), (iii) and (iv).
Therefore, maximum or minimum value of objective function ‘Z’ exist on end points of line (constraint) (i) in feasible region i.e., at A or B.
At A (3, 2) Z = 5 × 3 + 8 × 2 = 15 + 16 = 31
At B (0, 5) Z = 5 × 0 + 8 × 5 = 0 + 40 = 40
Hence, cost of brick is minimum when 3 kg of B1 and 2 kg of B2 are taken.