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

Answer

N/a

Explanation

Let the firm has x number or large vans and y number of small vans. From the gives, information we have following corresponding constraint table.

Thus, we see that objective function for minimum cost is Z=400x+200y.
Subject to constraints `200x+80y ge 2000["pakage constranit"]`
`Rightarrow 5x+2y ge 30....(i)`
and `400x+200y le 3000["cost constraint"]`
`Rightarrow 2x+y le 15 ...(ii)`
and `x le y ..["van constraint"]...(iii)`
and `x ge 0, y ge 0 ["non negative constraints"]...(iv)`
Thus, required LPP to minimise cost is minimise `Z=400x+200y, "subject to " 5x+2y ge 30`
`2x+y le 15`
`x le y`
`x ge 0, y ge 0`