A firm has to tra

Let the firm has x number of large vans and y number of small vans. We make the following table from the given data:

Thus according to the table, the cost becomes, Z=400x+200y

Now, we have to minimize the cost, i.e., minimize Z=400x+200y

The constraints so obtained, i.e., subject to the constraints,

200x+80y≥ 1200

Now will divide throughout by 40, we get

⇒ 5x+2y≥ 30…………..(i)

And 400x+200y≤3000

Now will divide throughout by 200, we get

⇒ 2x+y≤ 15…………..(ii)

Also given the number of large vans cannot exceed the number of small vans

⇒ x≤ y……………..(iii)

And x≥0, y≥0 [non-negative constraint]

So, minimize cost we have to minimize Z=400x+200y subject to

5x+2y≥ 30

2x+y≤ 15

x≤ y

x≥0, y≥0