Question

A haulage company receives an order to transport 1600 packages. They have large vans which can take 200 packages, and cost $40 a journey to run. They also have small vans which can take 80 packages, and cost $20 each to run for the same journey. It is required that not more than $340 be spent on running the vans, and also that the number of small vans used must not exceed the number of large vans. How many of each van should be used to keep costs as low as possible?

Answer 1

The company needs to transport 1600 packages.

Large vans can take 200 packages and cost is $40.

Small vans can take 80 packages and cost $20.

The total cost should not be more than $340.

The problem can be solved by trial and error method.

Suppose we take 6 Large vans.

Total packages = 6 x 200 = 1200 and Total cost = 6 x $40 = $240

Remaining no. of packages = 1600 - 1200 = 400

Remaining amount of money left = 340 - 240 = $100

Now,

Suppose we take 5 small vans

No. of packages transported = 80 x 5 = 400

Amount of money = $20 x 5 = $100

Thus it fits in the exact value as required.

Therefore, we need to select 6 large vans and 5 small vans.

Also it can be seen that the no. of small vans is lesser than the large vans.