Q12 of 45 Page 250

A firm has to transport 1200 packages using large vans which can carry 200packages each and small vans which can take 80 packages each. The cost for engaging each large van is Rs 400 and each small van is Rs 200. Not more than Rs 3000 is to be spent on the job and the number of large vans cannot exceed the number of small vans. Formulate this problem as a LPP given that the objective is to minimise cost.

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


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