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 ?
Answer & explanation
Correct answer: option 4
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,
$x,y≥0$