wxmaxima
at which prices will make maximum profit if the demand function is q(x)=8.8*(sqrt(21-0.3*p^^2)).
thank you
To find the prices at which the maximum profit will be made, we need to consider the revenue and cost functions as well. The revenue function is given by R(x) = p * q(x), where p is the price and q(x) is the demand function. The cost function represents the cost of producing the goods.
Since we don't have the exact cost function, we'll assume it as a constant, C. Therefore, the profit function, P(x), can be defined as P(x) = R(x) - C.
Now, let's go through the steps to find the prices that will maximize the profit:
1. Substitute the given demand function, q(x) = 8.8 * sqrt(21 - 0.3 * p^2), into the revenue function:
R(x) = p * q(x) = p * (8.8 * sqrt(21 - 0.3 * p^2))
2. Simplify the revenue function:
R(x) = 8.8p * sqrt(21 - 0.3 * p^2)
3. Determine the profit function:
P(x) = R(x) - C = 8.8p * sqrt(21 - 0.3 * p^2) - C
To find the prices that maximize profit, we need to find the critical points of the profit function. These critical points occur when the derivative of the profit function is equal to zero.
4. Calculate the derivative of the profit function:
dP(x)/dp = 0
5. Solve the derivative equation for p to find the critical points.
6. Once you have the critical points, evaluate the profit function at each critical point to determine the maximum profit.
By following these steps, you can determine the prices at which the maximum profit will be made using the given demand function.