The equation of total cost is the integral of MC:
TC=1/3×Q3+14Q2+211Q+10.
The equation of total revenue is:
TR=AR×Q=200Q−8Q2.
An expression for profit is π=TR−TC=−1/3×Q3−22Q2−11Q−10.
The equation of marginal revenue is:
MR=TR′(Q)=200−16Q.
The level of output that maximizes profit is at
MR = MC,
Q2+28Q+211=200−16Q,
Q2+44Q+1=0, Q1=2−44+43.95=−0.025,
Q2=2−44−43.95=−43.98.
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