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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 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 minimize cost.

Here the solution is also given. But I am not understanding why is the restriction for cost (2nd restriction) $400x+200y≥3000$ ? It seems to me $400x+200y\le3000$ is appropriate. Am I doing wrong?

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You are correct. $400x + 200 y \leq 3000$ is the correct inequality.

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  • $\begingroup$ I have edited $y$ in the correct inequality. One more question: Is the $200x+80y≥1200$ inequality correct. I think yes. But a little bit confused. $\endgroup$ – time Nov 1 '15 at 5:39
  • $\begingroup$ @time : You could have made that question part of your original post... Since the $x$ large vans and $y$ small vans carry $200x+80y$ packages and they must carry at least $1200$ packages, that inequality is correct. $\endgroup$ – Eric Towers Nov 1 '15 at 5:50
  • $\begingroup$ You have a typo. It is $400x+200y\leq 3000$ $\endgroup$ – callculus Nov 1 '15 at 5:57
  • $\begingroup$ @calculus : True. Now it and the one in the OP are fixed. $\endgroup$ – Eric Towers Nov 1 '15 at 6:09

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