A firm wishes to transport 1500 packages using large vans which carry 100 packages each and small vans which can carry 50 packages each. The cost of engaging large van is ₹400 and small van is ₹100 and not more than ₹5,000 can be spent on job. Also, number of large vans can't exceed the number of small vans. Formulating an LPP we get ?

$2x+y≤30; 4x+y ≤50; x ≤ y; x, y ≥ 0$

The correct answer is Option (4) → $2x+y≤30; 4x+y ≤50; x ≤ y; x, y ≥ 0$

let $x$ = number of large vans

$y$ = number of small vans

Minimize = $Z=400x+100y$

As, the firm wants to minimize the total cost of hiring

Since 1500 package need to be transported;

$100x+50y≥1500$

$⇒2x+y≥30$

The total cost should not excced Rs. 5,000

$400x+100y≤5000$

$4x+y≤50$

Number of large vans cannot exceed small vans, $x≤y$

and,

$x,y≥0$