1. The problem statement, all variables and given/known data A multi-product firm has total cost function C(q) = qtAq and faces inter-related but linear demand schedules for the n goods it produces: q = Bp + c. Both A and B are symmetric and B is invertible. Obtain an expression for total profit π(q) in the form π(q) = qtDq - etq where D and e are appropriate matrices. 2. Relevant equations We are given that Total Cost is, C(q) = qtAq. We also are given a production function: q = Bp + c Total profits is just Total Revenue, p*q, minus Total Costs. Hence: π = p*q - C(q). And we want to get it into a form like this: π(q) = qtDq - etq 3. The attempt at a solution So far I have done some manipulation of the production function: q = Bp+c B-1(q-c)=p and then substituted into the equation: π(q) = p*q-C(q) = (B-1(q-c))q - qtAq The remaining dificulities I'm having is figuring out how to get this resulting equation to look something like the requested, π(q) = qtDq - etq. I'm also not sure if the algebra is fully legal. While I know this isn't Physics, it's really just math. The only econ part of it is in the word problem and equation definitions. If you could help at all I would be most appreciative. If you need any more info please let me know. Thanks!