Suppose a competitive firm has as its total cost function: TC=23+3q^2 Suppose the firm's output can be sold (in integer

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Suppose a competitive firm has as its total cost function:
TC=23+3q^2
Suppose the firm's output can be sold (in integer units) at $72per unit.
Use calculus and formulas to find a solution (don't justbuild a table in a spreadsheet as in the previouslesson).
Hint 1: The first derivative of the totalprofit function, which is cumulative, is the marginal profitfunction, which is incremental. The lecture and formula summaryexplain how to compute the derivative.
Set the marginal profit equal to zero to define an equation forthe optimal quantity q.
Hint 2: When computing the total profitfor a candidate quantity, use the total profit function you define(rather than summing the marginal profits using the marginal profitfunction).
How many integer units should the firm produce tomaximize profit?
Please specify your answer as an integer. In thecase of equal profit from rounding up and down for a non-integerinitial solution quantity, proceed with the higherquantity.
What is the total profit at the optimal integer outputlevel?
Please specify your answer as an integer.