Farmer John needs to know how many bags of fertilizer (F) to use. He knows from experience that his output of wheat (Q, in bushels) is Q=4F0.5. A bushel of wheat sells for p=$8 and a bag of fertilizer costs w=$4.

Take the general expression for profit (=pQwF) and replace Q with the expression for the production function. You Farmer John needs to know how many bags of fertilizer (F) to use. He knows from experience that his output of wheat (Q, in bushels) is Q=4F0.5. A bushel of wheat sells for p=$8 and a bag of fertilizer costs w=$4. Take the general expression for profit (=pQwF) and replace Q with the expression for the production function. You should then obtain a profit function that depends only on F (and not on Q). Then use calculus to find the profit-maximizing amount of fertilizer. Finally, calculate the corresponding quantity of wheat producedstep by step.