Let’s consider x and y to be the number of large and small vans respectively.
From the given information the below constrains table is constructed:
Now, the objective function for minimum cost is
Z = 400x + 200y
Subject to the constrains;
200x + 80y ≥ 1200 ⇒ 5x + 2y ≥ 30 ….. (i)
400x + 200y ≤ 3000 ⇒ 2x + y ≤ 15 ….. (ii)
x ≤ y …. (iii)
and x ≥ 0, y ≥ 0 (non-negative constraints)
Therefore, the required LPP is to minimize Z = 400x + 200y
Subject to the constraints 5x + 2y ≥ 30, 2x + y ≤ 15, x ≤ y and x ≥ 0, y ≥ 0.