Objective function with two variables A factory produces jointly two articles, and it has the problem to decide their prices in order to maximize the monthly income, knowing that the demand d1 (in hundreds of units) of the first article is given by the following function:
d1 (p1, p2) = 100 - 10 * p1 + 2 * p2
and knowing that the demand d2 (in hundreds of units) of the second article is given by the following function:
d2 (p1, p2) = 150 + 2 * p1 - 10 * p2
where p1 and p2 are the unit prices respectively of the first article and of the second article.
My book gives the following answers: p1 = Euro 6,77 and p2 = Euro 8,85
How could I solve this problem?
Thank you for considering my question

The turnover related to product 1 is: $e_1(p_1,p_2)=d_1(p_1,p_2)\cdot p_1$
The turnover related to product 2 is: $e_2(p_1,p_2)=d_2(p_1,p_2)\cdot p_2$
And the total turnover  is $e_{1,2}(p_1,p_2)=e_1+e_2$
Now you differentiate $e_{1,2}(p_1,p_2)$ in respect to $p_1$ and $p_2$ and set the derivatives equal to zero.
$\frac{\partial e_{12}}{\partial p_1}=0$
$\frac{\partial e_{12}}{\partial p_2}=0$
Solve this eqaution system for $p_1$ and $p_2$.
