Question: A Lumber Yard gets lumber in 25 ft lengths from a nearby sawmill. These are cut into standard and custom lengths to fill orders. The lumberyard has received an order for 700 7ft boards, 1200 9ft boards and 300 10ft boards and has none of these lengths currently available.

What is the minimum number of 25 ft boards which must be ordered to meet this order (Hint: first determine the number of different ways a 25 ft board can be sawn into 7, 9 and 10 ft boards with some wastage allowed (there are 6))