Loading subjects
Linear Programming · Part 1 of 3
3 exam-style questions with model answers, plus 4 quick multi-choice questions — every question on this part of the standard, grouped by the 1 page of notes they come from.
Write a full answer before you reveal the model one. That comparison is where the learning happens.
A joinery makes doors and window frames. A door needs 3 hours of machining and 2 hours of finishing; a frame needs 2 hours of machining and 4 hours of finishing. There are 60 machining hours and 80 finishing hours available. Doors sell at $180 profit, frames at $150. Formulate the linear programme.
An orchard packs two box types. A standard box holds 8 kg and takes 4 minutes to pack; a premium box holds 5 kg and takes 9 minutes. There is one shift of 6 hours of packing labour and 900 kg of fruit available. The orchard must pack at least twice as many standard boxes as premium ones, and has a contract for at least 20 premium boxes. Standard boxes return $6 each and premium $11. Formulate the model and explain how you translated the ratio and contract conditions.
A transport firm must move at least 500 tonnes of freight using small trucks (8 t, $220 per trip, 1 driver) and large trucks (20 t, $480 per trip, 2 drivers). At most 30 trips can be scheduled and at most 45 drivers are available. Formulate the model to minimise cost, and critically evaluate the four standard linear programming assumptions in this context.