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 iob 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.
Solution:
Suppose
and
to be the number of large and small vans respectively. The below constrains table is constructed from the information provided:
![Rendered by QuickLaTeX.com \[\begin{tabular}{|l|l|l|l|} \hline Items & Large vans $(\mathrm{x})$ & Small vans $(\mathrm{y})$ & Maximum/Minimum \\ \hline Packages & 200 & 80 & 1200 \\ \hline Cost & 400 & 200 & 3000 \\ \hline \end{tabular}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-c89afff87b9f4684215deaf8408ca108_l3.png)
The objective function for minimum cost is ![Rendered by QuickLaTeX.com \mathrm{Z}=400 \mathrm{x}+200 \mathrm{y}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2e18a77539207cd001485fa7ae9cb52d_l3.png)
Subiect to the constrains:
(i)
(ii)
y …. (iii)
and
(non-neqative constraints)
Thus, the required LPP is to minimize ![Rendered by QuickLaTeX.com \mathrm{Z}=400 \mathrm{x}+200 \mathrm{y}](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2e18a77539207cd001485fa7ae9cb52d_l3.png)
Subject to the constraints
and ![Rendered by QuickLaTeX.com x \geq 0, y \geq 0](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-2241d51b2b3f36c0ccb560933283afc0_l3.png)