Question

Maximize: z = 3x₁ + 4x₂ subject to 2x₁ + x₂ ≤ 40, 2x₁ + 5x₂ ≤ 180, x₁, x₂ ≥ 0. In the LPP, which one of the following is feasible comer point?

(a) x₁ = 18, x₂ = 24

(b) x₁ = 15, x₂ = 30

(c) x₁ = 2.5, x₂ = 35

(d) x₁ = 20.5, x₂ = 1

Answer 1

(c) x₁ = 2.5, x₂ = 35

z = 3x₁ + 4x₂

Let us solve the equations

2x₁ + x₂ = 40 ... (1)

2x₁ + 5x₂ = 180 … (2)

(1) – (2) ⇒ -4x₂ = -140

x₂ = 35

We have 2x₁ + x₂ = 40

2x₁ + 35 = 40

2x₁ = 5

x₁ = 2.5