Coin-operated laundry facilities are a regular part of life for many people, especially those living in large cities. In 2017, the coin-operated laundry industry generated nearly $5 billion in gross revenue from about 29,500 locations nationwide, the majority of which are individually owned and operated (Data from Coin Laundry Association). Suppose that you own a coin-operated laundry. Right now, you charge $2.50 per washing machine load. Your current daily demand is 750 washing machine loads. In order to take advantage of this, you raised the price of the washing machines to $3.00 per load. However, once you did this, the daily demand for washing machines dropped to 625 loads. (Situation: Coin-Operated Laundry)

Washing Machine Operations
Daily Demand, x	Price per Load, p
750	$2.50
625	$3.00

What’s the deal? You raised the price and expected to make more money. Instead, you made the exact same amount. Assume that your price demanded function is linear in terms of x. That is p, price, is a linear function of x, number of loads of washing. Answer the following questions in a discussion post in Unit 1: Maximizing Profit Discussion Forum on Blackboard (under discussion in the left side menu of your Blackboard course).

Discussion Post: Analysis of Your Coin-Operated Laundry

Find the slope of the price function, p, in terms of x, loads of washing.

1. Use this slope and the point-slope formula to find the linear equation p(x).
2. Is the slope negative or positive? What does this mean in this context? That is, what does this say about the price of a load of washing? 
3. Think back to the definition of demand. Does this equation fit into this definition (we are using x for quantity instead of q)? Explain. 
4. Now that you have a price equation, find the equation for revenue, R(x).
5. After running your business for several years, you know that there are costs associated with running a coin-operated laundry. Give some examples of what fixed costs might be for this type of business. Give some examples of what some variable costs might be. Think outside the box! Don’t just list the examples from the section, give context. That is, “machines” is not an appropriate answer. What kind? How many? Etc. Don’t give actual costs (no outside research needed) but list what kinds of things might go into the costs of a business-like. Give three kinds of each type of cost (3 fixed and 3 variables) and explanations for each. Use complete sentences. This answer should be in paragraph form.
6. You examine all of the above costs and determine that your fixed costs are $256 per day and your variable costs are $0.65 per washing machine load (per x). What is your marginal cost? Use this information to write the daily cost function, C(x).
7. Now that you have the revenue and cost functions, find the daily profit function, P(x). 
8. According to your demand/price function, p(x), if you charged $1.75 per washing machine load, how many loads would be your daily demand? At this level, would you have profit loss or gain?
9. How many washing machine loads is your break-even point? At this x-value, what price p would you charge (use your price function, p(x))? 
10. We don’t just want to break even, right?! We want to make money in our business. To this end, find the x-value (daily number of washing machine loads) that maximizes profit. 
11. What is the maximum profit?
12. What price, p(x), do you need to set to gain this maximum profit? 
13. What do you think? Can you live on the proceeds of your coin-operated laundry? (Remember that this is DAILY profit) What things could you change to increase your profit? Give three examples. Use complete sentences. This answer should be in paragraph form. (Even if you answered yes to the previous question, answer this last one – it’s always good to increase profit!)
14. Discussion Post: Response to Another Student

Now that you have completed your discussion post, respond to another student’s discussion post. For numbers 2 and 3 here, comment as if you are a consulting firm that they have hired to help improve their business. You want to help them, not just criticize. You are trying to “sell” your help so remember to give your reasoning, be persuasive and professional. Your response to another student should include these three paragraphs, at least.

1. Take a look at their math. Did you do the problem in the same way? Are there any pointers you can offer? Did you realize that you made a mistake and they are correct?
2. Everyone will have different answers for #6. Look at their proposed variable and fixed costs. Do you agree? Is there anything you didn’t think of? Comment on what they choose to discuss and their reasoning. 
3. Everyone will have different answers for #14. Comment on their answers. Do you agree? Is there anything you didn’t think of? Discuss their methods of increasing profit. Do you think they would work? How would you change or improve them?
4. In this discussion, you will be utilizing your skills to build revenue, cost, and profit functions, determine the break-even point, maximum profit, and answering some discussion questions.