Question

Following is the profit function for a firm selling two products:
π=50X-X2+100Y-4Y2
Where X and Y represent output rates of products 1 and 2, respectively
Determine the profit maximizing output rates for the two products and the profit associated with these output rates

Answer 1

$$\frac {\delta {\pi}}{\delta x}=50-2x$$

$$\frac {\delta {\pi}}{\delta x}=100-8y$$

$$50-2x=0$$

$$x=25$$

$$100-8y=0$$

$$y=12.5$$