A company has a fixed cost of $$30,000$ and a production cost of $$10$ for each pair of sunglasses it manufactures. Each pair of sunglasses sells for $$15.$

a$)$ What are the cost, revenue, and profit functions?

b$)$ Find the profit $($loss$)$ corresponding to production levels of $5000$ and $10000$ units, respectively.

c$)$ Sketch a graph of the cost and revenue functions.

d$)$ Find the break$-$even point for the company algebraically.

Solution:

a$)$

b$)$

c$)$

d$)$