Using data from past years, the economists for smith brothers inc determined that the revenue f the company can be modeled by the function R(x)=0.0125x^2+412x. In addition, the function C(x)=12225+0.00135x^2 models the total cost of doing business, where x us v the number of customers patronizing the business in both functions.

A) how many customers just there be for ssmithmith bros inc to realize am annual profit of $60000?

I have no idea how to do modeling Function

what do you mean by "do" the function? They gave it to you.

Surely you know that profit = revenue-cost, and they gave you both of those, so

P(x) = R(x)-C(x)
= 0.0125x^2+412x - (12225+0.00135x^2)
= 0.01115x^2 + 412x - 12225

So when does P(x)=60000? when x=174.48

so, they need 175 customers to make at least 60,000 profit.

See? Not so complicated, once you get past all the words.

To determine the number of customers required for Smith Brothers Inc to realize an annual profit of $60,000, we need to find the revenue (R(x)) and cost (C(x)) functions for the company.

Given:
Revenue function: R(x) = 0.0125x^2 + 412x
Cost function: C(x) = 12225 + 0.00135x^2

To find the profit function, we subtract the cost function from the revenue function:
Profit function: P(x) = R(x) - C(x)

Since profit is equal to $60,000, we can write the equation as:
P(x) = 60000

To solve for x, we substitute the revenue and cost functions into the profit equation:
0.0125x^2 + 412x - (12225 + 0.00135x^2) = 60000

Now, simplify the equation:
0.0125x^2 + 412x - 12225 - 0.00135x^2 = 60000

Combine like terms:
0.01115x^2 + 412x - 12225 = 60000

Rearrange the equation:
0.01115x^2 + 412x - 72225 = 0

Now, we have a quadratic equation in terms of x. We can solve this equation by factoring, completing the square, or using the quadratic formula.

Once you have solved the quadratic equation, you will have the values of x. Select the positive value, as the number of customers cannot be negative.

Therefore, the number of customers required for Smith Brothers Inc to realize an annual profit of $60,000 will be the positive value obtained from solving the quadratic equation.