Please assist with the given solution regarding production and maximum provide. Provide step by step calculations in the completed solution.
A firm produces two goods 1 and 2 and has the following cost function
C = 10Q1 + Q1Q2 + 10Q2
Where Q1 and Q2 denote quantities of good 1 and 2. P1 and P2 denote the corresponding prices and the demand functions are:
P1 = 50 - Q1 + Q2
P2 = 30 + 2Q1 - Q2
Determine the maximum profit if the firm in total produces 15 units, that is if Q1 + Q2 = 15.