Further Mathemtics

[tiger2012]

Does any one know how to work out this problem and the solving problem is from Further Mathematics and it is from"Linear Programming"
This is the question
The army is required to airlift 450 people and 36 tonnes of baggage by helicopter. There are 9 Redhawk helicopters and 6 Blackjacket helicopters available. Each Redhawk can carry 45 passengers and 3 tonnes of baggage,while each blackjacket can carry 30 passengers and 4 tonnes of baggage. Running costs per hour are $1800 for each Reshawk and $1600 for each Blackjacket.

If the army wishes to minimise the costs of the airlift per hour, use a graphical method to find how many of each helicopter should be used.
If any one know answer to this question please reply with the answer and the work out.

[plato]

I think this is less of a linear programming exercise since there are few inequations.
Let B = No of Blackjackets needed and R= No of Redhawks needed.
R <= 9  and B<=6

450 people means   30B+45R=450
AND
36 tonnes means     4B+3R = 36
These are equations rather than inequations as ALL 450 people and ALL 36 tonnes must be shifted.
These produce two straight lines that intersect at B = 3 and R = 8. This is the solution for the number of each chopper required and meets the constraints R <= 9  and B<=6

The Cost of running these is given by  C = 1600B + 1800R
Sub in B = 3 and R = 8
This gives me  Cost = $19 200 per hour.

I don't think this can be minimised any further by increasing the number of one helicopter over the other as I assume that all of the cargo and people, not just "up to" 450 people or 36 tonnes of cargo, must be moved.
Realistically, one could look at using one chopper for cargo and the other for people until one becomes available to transport the other group but there is not enough information to look at that here.

Does anyone else have any ideas?