optimization help?

Question

a.) If a farmer plants x units of wheat in his field 0 ≤ x ≤ 196, the yield will be 14x-x^2/14 How much wheat should he plant for the maximum yield?

 

b.) In the problem above, it costs the farmer $108 for each unit of wheat he plants, and he is able to sell each unit he harvests for $84. How much should he plant to maximize his profit?

Answer 1

Part a: the graph is a parabola with a maximum at its vertex. Use the vertex formula x=-b/(2a) to find what x value this occurs at.

 

Part b: Develop the formula for Profit, from the statement provided.

Then use Calculus method(s), e.g. setting first derivative to 0, to find critical values, etc.

You can also check this using a graphing calculator.