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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 $₹ 400$ 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 as a LPP given that the objective is to minimise cost.
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Let the firm has $x$ number of large vans and $y$ number of small vans then.
\begin{array}{|lccc|}
\hline & Large vans(x) & Small vans (y) & Maximum/ Minimum \\
\hline Packages & 200 & 80 & 1200 \\
Cost & 400 & 200 & 3000 \\
\hline
\end{array}
$\mathrm{Z}=400 \mathrm{x}+200 \mathrm{y}$ (to be minimised)
Subject to constrainst
Thus, required LPP to minimise cost is minimise $Z=400 x+200 y$, subject to $5 x+2 y \geq 30$.
$\begin{aligned} 2 x+y & \leq 15 \\ & x \leq y \\ & x \geq 0, y \geq 0 \end{aligned}$
\begin{array}{|lccc|}
\hline & Large vans(x) & Small vans (y) & Maximum/ Minimum \\
\hline Packages & 200 & 80 & 1200 \\
Cost & 400 & 200 & 3000 \\
\hline
\end{array}
$\mathrm{Z}=400 \mathrm{x}+200 \mathrm{y}$ (to be minimised)
Subject to constrainst
Thus, required LPP to minimise cost is minimise $Z=400 x+200 y$, subject to $5 x+2 y \geq 30$.
$\begin{aligned} 2 x+y & \leq 15 \\ & x \leq y \\ & x \geq 0, y \geq 0 \end{aligned}$
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