Q. Assume you hire a furloughed Wall Street analyst to help you analyze your manufacturing process also she uses your historical cost records to approximate that your total cost function is C(Q) = 100 + 2Q + 3.5Q2. Using this equation, answer the following and explain how your logic and calculations.

a. Explain how more is your firm's profit or loss at an output of zero? Elucidate.

At zero output cost C (Q=0) =100+2*0+3*0^2=100
Revenue = Price*0 units = 0
Profits = Revenues - cost = 0-100= -100 (loss of 100)

b. With the above cost equation, average total costs (ATC), first decline as output increases, and then begin to rise. Assuming output occurs in whole units, i.e. 1, 2, 3... at Illustrate what output does the low point of ATC occur and illustrate what is the ATC at that output? Explain how your calculations.

ATC=C (Q)/Q=100/Q+2+3Q
For minimization differentiate w.r.t. Q and equate to zero the equation is -100/Q^2+3=0 and the answer is Q=5.77
Since Q can take only whole units, calculating ATC at Q=5 comes out to C(Q=5)=100/5+2+3*5=37. When ATC is Compute d at Q=6, it comes out to C(Q=6)=100/6+2+3*6=36.67. Since cost is minimum at Q=6, the ATC is minimized at Q=6.

c. Illustrate what is the total cost of an output of 500?