Suppose that you can sell as much of a product (in integer units) as you like at $74 per unit. Your marginal cost (MC) for producing the qth unit is given by:
MC=8q
If fixed costs are $450, what is the profit at the optimal integer output level?
I solved the question using two different methods- Excel and integral function-that generated two different results. For the Excel function, I simply listed all the data, MC, TC, MR etc. very basic, and I got (-144). For the integral function, I used TC= 4*q^2+450 to calculate the total cost, which got me (-108).
(-144) is clearly the right answer, as the total cost of producing one unit is by no means 454, as is the result of substituting 1 into the TC formula. Can you advise if I had missed any assumptions while using the integral function approach? why the different results. Thank you in advance.