Break Even Calculus Problem

Question

The revenue from producing electric bicycles can be modeled by the function and their cost can be modeled by the function where q is the number of thousands of electric bicycles sold/produced and costs and revenues are in thousands of dollars. How many thousands of electric bicycles should the manufacturer need to break even?

Answer 1

R(q) = C(q); q²(197.2 - 2.8q) = 589.1 + 57.9q; 2.8q³ - 197.2q² + 57.9q + 589.1;

q = 1.91 thousands of electric bycicles for break even

Answer 2

The answer is 2000 units, where profit (revenue - total expenses) start to become positive.

This can be simply implemented (e.g. in excel) by P(q)= R(q) - C(q) where P(q) is <0 for for q<2 and P(q)>0 for q ≥ 2.