Algebraic solution to fruit dealer optimisation problem
Channel: David Roberts
Date: 08/05/2014

This is the rest of the solution of the problem considered in lectures, and which is detailed on page 60 of your notes (and reproduced below). Here we solve the optimisation problem by finding the vertices of a convex region in R^3 via the algebraic method.

==== Problem description ====

A fruit dealer can transport up to 800 boxes of fruit from Renmark to Adelaide on a truck. He must transport at least 200 boxes of oranges, at least 100 boxes of grapefruit and at most 200 boxes of tangerines. The profit per box is $2 for oranges, $1 for grapefruit, and $3 for tangerines. How many boxes of each kind of fruit should be loaded onto the truck in order to maximise profit?