Question

Ahmed is a football producer who is interested in knowing that at which level of production his profit would be maximized. If following is the production function determine at which quantity the profits would be maximized.

Y=10+10X+10X²

Answer 1

The maximum of profits will be when the product function is maximum:

$$\dfrac{dY}{dX}=0,$$ $$\dfrac{d}{dx}(10+10X-10X^2)=10-20X=0,$$ $$X=0.5$$

Therefore, at $X=0.5$ the profits would be maximized.