Question

A hauling company receives an order to transport 120 packages. They have large vans which can take 15 packages, and cost $6 a journey to run. They also have small vans which takes 5 packages, and cost $4 each to run for the same journey. It is required that more than $60 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?

a.) if the cost of a small van run reduced to $1, would it change the optimal solution?

b.) if the cost of a small van run reduced to $2, would it change the optimal solution?

c.) what if we had a $1000 to spend on running packages, would it change the optimal solution?

Answer 1

Solution

The Hauling Company should use the following number of vans in order to transport 120 packages, given the above conditions:

Large Vans - 6 [Costing a total of $36 (6 vans * $6)]

Small Vans - 6 [Costing a total of $24 (6 vans * $4)]

Total cost - $60 ($36 + $24)

Solution to A and B

If the cost of a small van reduces to $1 or $2, the optimal solution will remain the same. Also, if the cost of small vans reduces to $1 or $2, the condition of spending more than 60$ cannot be met in any given scenario.

Solution to C

Even if we had a $1000 to spend on packages, it will not change the solution as the maximum cost will be $48 (8 large vans * $6) which will be able to transport 120 packages.