How to solve this Marginal Analysis question

Question

Suppose the total cost in dollars per week by Capital Corporation for producing its best-selling product is given by 𝐶(𝑥)=1000+300𝑥.The revenue function for the production of the product  was  derived  to  be 𝑅(𝑥)=800𝑥−0.6𝑥2.  Analyse  the  profit  function for  the manufacturing of 𝑥 products, as well as interpret what the marginal cost and marginal revenue of 15 products signifies. Additionally, determine the exact and approximate profit from the manufacturing of the 42^nd product.

Answer 1

C(x) = 1000 + 300x

R(x) = 800x- 0.6x^2

Marginal cost = MC = 300

marginal cost of 15 products or any number of products is 300

Marginal revenue = MR = 800 =1.2x

marginal revenue of 15 products = 800-1.2(15) = 800- 18 = 782

Profit = P = R-C = 500x -0.6x^2 - 1000

Profit for 42 = 500(42) - 0.6(42^2) -1000 = 21000 -1058.4 -1000 = 18941.6