If total revenue of a firm is 5Q^2 4Q+10 and total cost is 4Q^2 6Q+20 , find the total profit.

Total profit is calculated as the difference between total revenue (TR) and total cost (TC).

Given: $$\text{TR}=5Q^2-4Q+10$$ $$\text{TC}=4Q^2-6Q+20$$

The formula for total profit ($\pi$) is: $$\pi =\text{TR}-\text{TC}$$

Substitute the given expressions: $$\pi =(5Q^2-4Q+10)-(4Q^2-6Q+20)$$

Simplify the equation: $$\pi =5Q^2-4Q+10-4Q^2+6Q-20$$ $$\pi =(5Q^2-4Q^2)+(-4Q+6Q)+(10-20)$$ $$\pi =Q^2+2Q-10$$

Thus, the total profit function is: $$\boxed{\pi =Q^2+2Q-10}$$