Question

When Farmer Hoglund applies N pounds of fertilizer per acre, the marginal product of fertilizer is 1 -N/200 bushels of corn. If the price of corn is $4 per bushel and the price of fertilizer is $1.20 per pound, then how many pounds of fertilizer per acre should Farmer Hoglund use in order to maximize his profits?

I already know the answer, I was just hoping for some help on the steps.

Answer 1

to maximize profit, farmer must use 0.208 pounds of fertilizers

Step-by-step explanation:

For profit maximization, marginal revenue must be equal to marginal cost.

Here marginal product of fertilizer= 1-N/200

selling price per busher= $4

total marginal revenue= (1-N/200)× 4

Total cost of fertilizer= 1.2N

To maximize profit

Marginal cost= marginal revenue

1.2N= (1-N/200)× 4

4.8N= 1-N/200

N= 0.208 pounds

to maximize profit, farmer must use than 0.208 pounds of fertilizers

Answer 2

N Pounds = 140 to maximize profits

Step-by-step explanation:

To Maximize profit : Marginal cost equal marginal Revenue

the point where no extra unit can be produced.

1.20*N = (1-N/200)*4

Step 1 : Divide by $4 on both sides to cancel the $4 on the right hand side

0.3N =1-N/200

Step 2 : Minus 1 on both sides to cancel the 1 on the right hand side

-0.7N = -N/200

Step 3 : Multiply by 200 on both sides to cancel the 200 denominator on the right hand side

-140 = -N

Step 4 : N cannot be negative, therefore multiply by -1 on both sides

N =140