I am given that:
TC = 1/3Q³-7Q²+111Q+50
Find output and price that maximise profit and then calculate profit. Ensure you have found a maximum and checked for boundary maxima.
So far I have done this:
Rearranged Q so that
Q*P = TR = -Q+100 (Q) = -Q²+100Q
Profit = TR-TC= -Q²+100Q-1/3Q³-7Q²+111Q+50
First Derivative = -Q²-12Q-11
Therefore Q=11 or Q=-1
Then Used Second Deriv to work out Min/Max:
When Q=11, Maximum
When Q=-1, Maximum
Now I am unsure If I have made a mistake up to this point however I sort of come stuck here. Does anyone know if I have made any mistakes and what the next step would be?
My thought is that you cant have a negative quantity and therefore Q must = 11. When Q = 11, P=89
and then i was just going to plug the figures into the Profit formula and see what i get?!