A fictional track diagram needs 24 segments in the ratio 3 short: 1 long. Shorts are 1/3 m each and longs are 3/4 m each. Supplier A sells whole metre units at $1.10/m and B at $1/m. All tape is usable, joins are allowed and cutting loss is zero. There are no initial fees. Budget is $11.20. Spare length may be kept.
Your task
Find both counts, the short fraction of all segments and the exact total length. Calculate cheapest sufficient whole-metre quantities, total cost and spare length for each supplier. Recommend an order within the budget or explain why neither works. State one assumption.