The total revenue and the total cost (in dollars) for the production and sale of steel-toe boots are given, respectively, by R(q) = 0.2q 2 + 200q and C(q) = 24q + 21900.

a. Find the value of q where the graph of R(q) has a tangent line that is horizontal.

b. Find the profit function (q).

c. Find the values of q at which there are break-even points, if any.

d. Find the value of q where the graph of (q) is maximum