How many integer units should the firm produce to maximize profit and what is the total profit at the optimal integer output level?....

Assume that a competitive rm has the total cost function: TC : 193 401:;2 + 840g + 1800 Suppose the price of the rm's output (sold in integer units) is $750 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 rst derivative of the total prot function, which is cumulative, is the marginal prot function, which is incremental. The lecture and formula summary explain howr to compute the derivative. Set the marginal profit equal to zero to dene an equation for the optimal quantity q. Rearrange the equation to the quadratic form aq2 + bq + c = 0, where a, b, and c represent numbers. Use the quadratic formula to solve for q: _ I:I:l:1_/lzv2 4ac q_ 2:; For non-integer quantity, round up and down to nd the integer quantity with the optimal prot. Hint 2: When computing the total profit for each candidate quantity, use the total profit function you dene (rather than summing the marginal prots using the marginal prot function)