. The company Spacely Sprockets produces sprockets. They have fixed equipment costs of $10,000 and it costs the company $50 to produce each sprocket.

(a) Find the cost function.

(b) Graph the cost function using Desmos. Adjust the viewing window so that the graph is visible. Save your graph.

(c) Is the graph increasing or decreasing?

(d) Find the y-intercept.

(e) Interpret the y-intercept in the context of this problem.

2. Spacely Sprockets from question #1 sells their sprockets for $100 each.

(a) Find the revenue function.

(b) Using the cost function from #1a and the revenue function from #2a, find the profit function.

(c) Graph the profit function using Desmos. Adjust the viewing window so that the graph is visible. Save your graph.

(d) Find the x-intercept of the profit function.

(e) Interpret the x-intercept in the context of this problem.

(f) How many sprockets does Spacely Sprockets need to produce and sell to have a profit of $50,000?