In Baggs, Wyoming, cattle can be produced according to the following process: C = G/20 + P/40, where C is the number of cattle, G are bushels of grain, and P are acres of pasture.If grain costs $4 per bushel and pasture costs $3 per acre, how many cattle can Rancher Roy produce with a budget of $6,000?

Question

Quizplus · Accepted Answer

First, we need to rewrite the production function in terms of prices:

C = min(F1/20, F1F1/40) where G = F1*4 and P = F1F1*3

We have a budget of $6,000, so:

G + P = 6000

F1*4 + F1F1*3 = 6000

We can solve for F1:

F1 = (6000 - 3xF1F1) / 4

Substituting F1 into the production function:

C = min(((6000 - 3xF1F1) / 80), (6000 - 3xF1F1) / 1600)

To maximize the number of cattle, we want to maximize the output of the production function. Taking the derivative with respect to F1F1 and setting it equal to 0:

dC/dF1F1 = (9/1600) - (3/80) = 0

Solving for F1F1:

F1F1 = 60

Substituting back into the budget equation to find G and P:

G = F1*4 = 240
P = F1F1*3 = 180

Therefore, Rancher Roy can produce 75 cattle (the output of the production function when F1F1 = 60) with a budget of $6,000. Answer: D.

In Baggs, Wyoming, Cattle Can Be Produced According to the Following