Use the Total Revenue Function to find the revenue maximizing Price and Quantity. Use the profit function to find the pr

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Use the Total Revenue Function to find the revenue maximizing Price and Quantity.
Use the profit function to find the profit maximizing P and Q.
Use the Total Revenue and Total Cost functions to find the profit maximizing P and Q.
Explain briefly why these come to the same answer. (NOTE: Q = Quantity and P = Price)
Inverse Demand Function: P = 250 – 10Q
Total Revenue Function: TR = 250Q – 10Q2
Total Cost Function (this is a linear function): TC = 600 + 50 Q
Profit Function: Profit = 200Q – 10Q2 – 600