A firm produces two products with inverse demand functions P1=Q2Q1+a and P2=Q12Q2b. The cost function is C=Q12+2Q22+10. The profit function is Π= (Q2Q1+a)Q1 + (Q12Q2b)Q2 - (Q12+2Q22+10). The profit function has a maximum because it is continuous and differentiable. dadQ1 is negative and dadQ2 is positive, showing an increase in a decreases Q1 and increases Q2.