A firm estimates that the total revenue, $R$, in dollars, received from the sale of $q$ items (in thousands of items) is $R = 100000 \log(1+1000q^{2}).$ The manufacturing cost $C$, in dollars, of making $q$ thousand items is $C = 50000q.$
What is the cost of manufacturing per item? I am thinking if the equation is $50000q=100000 \log(1+1000q^{2})$, but I don't know how to solve it? Please guide me.
And what quantity should be produced to maximize profit? which I need the answer from this part to finish.
Thank you!