In a production form,it is estimated that the demand function for it's product is given by p=40q (1) At what level of production is revenue maximize (2) What is the maximum revenue at this point

The demand function is given by $p = 40q$.
Revenue $R$ is calculated as the product of price $p$ and quantity $q$:

$$R = p \times q$$

Substitute the given demand function into the revenue formula:

$$R = (40q) \times q$$ $$R = 40q^2$$

Note: A typical demand function shows that price decreases as quantity increases. The given function $p=40q$ implies that price increases with quantity, which is unusual for a demand function.

The revenue function is $R(q) = 40q^2$. This is a quadratic function representing a parabola that opens upwards.
For production levels $q \ge 0$, the value of $R(q)$ continuously increases as $q$ increases.
To find a maximum, we would typically take the derivative and set it to zero:

$$\frac{dR}{dq} = \frac{d}{dq}(40q^2) = 80q$$

Setting $\frac{dR}{dq} = 0$ gives $80q = 0$, which means $q = 0$. This corresponds to the minimum revenue ($R=0$), not a maximum.
Since the function $R(q) = 40q^2$ increases indefinitely for $q > 0$, there is no finite maximum revenue.

1) At what level of production is revenue maximized?
Based on the given demand function $p=40q$, the revenue function $R(q) = 40q^2$ continuously increases as the level of production $q$ increases (for $q \ge 0$). Therefore, there is no finite level of production at which revenue is maximized. Revenue can be made arbitrarily large by increasing production.

$$\boxed{\text{No finite level of production}}$$

2) What is the maximum revenue at this point?
Since there is no finite level of production that maximizes revenue, there is no finite maximum revenue.

$$\boxed{\text{No finite maximum revenue}}$$