Assume that a competitive firm has the total cost function: TC 1q-40q + 710q + 1700 %3D | Suppose the price of the firm's output (sold in integer units) is $550 per unit. Use calculus and formulas to find a solution (don't just build a table in a spreadsheet as in the previous lesson). Hint 1: The first derivative of the total profit function, which is cumulative, is the marginal profit function, which is incremental. The lecture and formula summary explain how to compute the derivative. Set the marginal profit equal to zero to define an equation for the optimal quantity q. Rearrange the equation to the quadratic form aq? + bq + c 0, where a, b, and c represent numbers. Use the quadratic formula to solve for q: -6+ vb2 - 4ac 2a For non-integer quantity, round up and down to find the integer quantity with the optimal profit. Hint 2: When computing the total profit for each candidate quantity, use the total profit function you define (rather than summing the marginal profits using the marginal profit function). Q: How many integer units should the firm produce to maximize profit? Please specify your answer as an integer. What is the total profit at the optimal integer output level? Please specify your answer as an integer.

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