Suppose a company produces and sells widgets. The demand for the widgets is given by the equation Qd = 200 - 4P, where Qd is the quantity demanded and P is the price of the widgets. The company's total cost function is given by TC = 100 + 50Q + 2Q^2, where TC is the total cost and Q is the quantity produced.

a) Determine the equilibrium price and quantity of widgets.

b) Determine the company's total revenue, total variable cost, and total profit at the equilibrium point.

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