Friday, September 26, 2008

The Farmer Bill's Problem

Every long journey begins with a first step. Starting our journey towards the science and technology of decision making, lets meet Bill, the farmer. He is facing one delicate problem. Can we help him?

Farmer Bill is planning his planting for the coming year. He expects to raise two crops: potatoes and wheat. He has 100 acres of land available for planting and will be able to devote 160 days of labor to his crops. He expects an acre of wheat to require four days of labor, while an acre of potatoes requires only one day.

He has $ 1100 that he can use for the start-up costs of planting and cultivating. It costs $ 10 an acre to plant and cultivate potatoes, while the corresponding costs for an acre of wheat are $ 20.

If Bill expects a revenue of $ 40 per acre of potatoes and $ 120 an acre for wheat, how many acres of each should he plant in order to achieve the highest possible revenue?

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