Question

A farmer is creating a whole farm plan for the upcoming production year. He has 800 acres of land available for crop production. He wants to maximize his gross margin of two crops, soybeans and corn. He believes that he can obtain a gross margin of $80 per acre of soybeans and $100 per acre of corn. He has 3500 available labor hours to allocate between the two crops and has determined that soybeans will require 2.5 hours of labor per acre while corn will require twice as much labor as soybeans. Soybeans will require $100 of operating capital per acre while corn will require operating capital equivalent to 150% of that of soybeans. $90,000 of total operating capital is available. What is the farmer's objective function?

	a.	Max = 80s + 100c
	b.	80s + 100c
	c.	s + c ≤ 800
	d.	Max Gross Margin = 80s + 100c

Answer 1

A farmer is creating a whole farm plan for the upcoming production year. He has 800 acres of land available for crop production. He wants to maximize his gross margin of two crops, soybeans and corn. He believes that he can obtain a gross margin of $80 per acre of soybeans and $100 per acre of corn.

As we know that an  objective function is a function that defines some quantity that should be minimized or maximized. Here the quantity is the gross margin which the farmer wants to maximize.

Here we have gross margin from soyabean = $80 per acre and the gross margin from corn = $100 per acre.

So total margin = ( $80 + $100 ), so we can write the objective function as --

Max Gross Margin = 80s + 100c

This is the main objective function, but this will be subjected to some constraints for example s+c must be less than or equal to 800 acres etc.