Suppose you are rancher, and you produce grass hay to feed to your cows over the...

Suppose you are rancher, and you produce grass hay to feed to your cows over the winter. You have already paid for all of your inputs for hay production, but you still need to make decision for the seeding rate (lbs/ac) and fertilizer rate (lbs/ac). You have determined the amount of hay production (tons/ac) you produce is characterized by the following equation:

?=0.05625? +0.1125? −0.00013?2−0.00178?21212

This also means that

??? x1= 0.05625 − 0.00026?1

???x2 = 0.1125 − 0.00356?2

Where

Y is the tons/ac of grass hay production

?1 is the seeding rate in lbs/ac
?2 is the fertilizer rate in lbs/ac

Also

?? = $145/???

??1 = $7.50/??

??2 = $1.50/??

Calculate the optimal amount of ?1 and ?2 you should use given the above information. (4 pts)
Calculate the profit at the optimal allocation of ?1 and ?2. (3 pts)
Now assume that you have a budget constraint set at $145. Give your budget constraint, calculate the optimal amount of ?1 and ?2 you should apply. (5 pts)
Calculate the profit at the optimal allocation of ?1 and ?2 from your answer in Part C. (3 pts)

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

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