Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers and y is the daily operating budget. a) dy/dx
b) Evaluate this derivative at x = 30 and y = 10,000 and interpret the answer.

Part A)

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

Where P is the number of eggs laid, x is the number of workers, and y is the daily operating budget (assuming in US dollars $).

A)

We want to find dy/dx.

So, let’s find our equation in terms of x. We can raise both sides to 10/7. Hence:

Simplify:

Divide both sides by the x term to acquire:

Take the derivative of both sides with respect to x:

Apply power rule. Note that P is simply a constant. Hence:

Simplify. Hence, our derivative is:

Part B)

We want to evaluate the derivative when x is 30 and when y is $10,000.

First, we will need to find P. Our original equations tells us that:

Hence, at x = 30 and at y = 10,000, P is:

Therefore, for our derivative, we will have:

Use a calculator. So:

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

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step-by-step explanation: