Supplies for the Battle of Hoth


Hoth Suppliers is a small manufacturer of 3 types of popular battle vehicles: the powerful At-At Walker, the fast Snow Speeder, and the lovable Tauntaun. Hoth Suppliers sells these vehicles to inhabitants on the war torn planet of Hoth (There are hardly any planets that are peaceful given the resistance from the Rebels against the Empire).

The manufacturing process consists of 4 principal departments: assembly, finishing, equipping, and feeding. The assembly department has 12 skilled droids, each of whom works 7 hours per day. The finishing department has 3 heavy duty droids, who also work a 7-hour shift each. The equipping department has 10 light duty droids who work 3 hours a day. And the feeding department is run by two nutrition specialists working 5 hours a day.

The production requirements for each vehicle are given in the table below, along with their profit margins. Because of the popularity of its products and limited production capacity (and it's Episode V), its products are in high demand, and Hoth can sell all it can produce each season. The company anticipates selling at least twice as many Snow Speeders as At-At Walkers.

How many of each vehicle should Hoth produce to maximise its profit?


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