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.

Home » 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.

CBSE | Class 12 | Linear Programming | Maths | NCERT Exemplar

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 $\mathrm{x}$ and $\mathrm{y}$ to be the number of large and small vans respectively. The below constrains table is constructed from the information provided:

$\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}$

The objective function for minimum cost is $\mathrm{Z}=400 \mathrm{x}+200 \mathrm{y}$

Subiect to the constrains:

$200 x+80 y \geq 1200 \Rightarrow 5 x+2 y \geq 30 \ldots \ldots$ (i) $400 x+200 y \leq 3000 \Rightarrow 2 x+y \leq 15 \ldots \ldots$ (ii) $\mathrm{x} \leq$ y …. (iii)
and $\mathrm{x} \geq 0, \mathrm{y} \geq 0$ (non-neqative constraints)