Question

The standard weight of a special purpose brick is 5 kg and it must contain two basic ingredients B₁ and B₂. B1costs Rs 5 per kg and B₂ costs Rs 8 per kg. Strength considerations dictate that the brick should contain not more than 4 kg of B₁ and minimum 2 kg of B₂. Since the demand for the product is likely to be related to the price of the brick, find the minimum cost of brick satisfying the above conditions. Formulate this situation as an LPP and solve it graphically.

Answer 1

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.