Songor Salt Manufacturing

Ltd produces two brands of salt identified as Medium size $($product $1)$ and Large size $($product $2)$ for the Ghanaian market.

The joint$-$cost

function

is

C$=392+5000+5$q$1$ where c c is the total cost of producing q$1$ units of $1$ and q$2$ units of

$2.$ The demand functions for these products are given by P$1=-2$q$1+205-02$ and P$2=-$q$1-92+153$ where PI and P$2$ are the prices of $1$ and $2,$ respectively. Find the number of units of medium size $($product $2)$ that Songor should produce to maximize its

profit