Let​ R(x), C(x), and​ P(x) be,​ respectively, the​ revenue,…

Let​ R(x), C(x), and​ P(x) be,​ respectively, the​ revenue, cost, and​ profit, in​ dollars, from the production and sale of x items. If ​ and ​, find each of the following. (a) = , the profit function. (b) = , the marginal profit. (c)   .

The marginal cost​ (in dollars per square​ foot) of installi…

The marginal cost​ (in dollars per square​ foot) of installing x square feet of kitchen countertop is given by . (a) Find the cost of installing 40 ft2 of countertop. (b) Find the cost of installing an extra 14 ft2 of countertop after 40 ft2 have already been installed.   Note: Round your answer to the nearest cent as needed.