Fred and Carrie's Research Report Washing Machine and Formula Information Fred and Carrie are thinking of purchasing washing machines that have a 20-pound capacity, meaning that each machine can hold 20 pounds or less. The inequalities below demonstrate the number of machines needed, based on the number of pounds of laundry a customer brings in (n.) M= number of washing machines needed n= number of pounds of laundry M= 1 2 3 4 5 if if if if if 0 20 40 60 80 < < < < < n n n n n 20 40 60 80 100 Fred and Carrie expect each load of laundry to cost them $0.97. Formula for cost per load (c) = .97*M Fred and Carrie plan to charge customers $12.00 per load. Formula for sales (s) = $12*M Profit is calculated by subtracting all costs from sales. Formula for profit per customer (P) = s-c Estimation and Reasonableness This section focuses on estimation and reasonableness. Use estimation and rounding for each of the questions in this section (numbers 1, 2 and 3). Fred and Carrie have two goals: Sell $2,500 or more per week. Spend $250 or less per week. 1. Are their goals reasonable? Why or why not? Be sure to show your work. The formula for sales (s) = $12*M 2500 = $12*M ____________ $12 $12 M=2500 ________ $12 250.00M = 208.33 Part 1 B The formula for cost per load (c) = .97*M 250= .97*M __________ .97 .97 M=250 ________ M=257.73 .97 Fred and Carries expectations are not feasible or reasonable as the company is limited to the amount of business, it can conduct during the timeframe. 2. If Fred and Carrie purchase 10 washing machines and each washing machine holds 20 pounds of laundry, is it reasonable to expect to wash 1,000 pounds of laundry in one week? Explain why or why not and show your work. If 10 machines = 20 lbs. C = 1000/(M*W) 10M*20=200 lbs. Then 1000lbs/200lbs= 5 hours When washing 1,000 lbs. of laundry a week it is reasonable considering each load of laundry will last for 1 hour and we are open for approximately 8 hours then each washer can hold 20 lbs. of laundry and we have 10 machines therefore in 5 hours we can complete 1,000lbs of laundry within 5 hours every day. 3. Fred and Carrie took out a loan for $100,000. Assuming they reach their goal of $2,500 in sales per week, what is a reasonable amount of time Fred and Carrie can expect it will take them to pay back the loan? Explain your reasoning and show your work. Note: Assume interest is fixed at 0.00% and the entire profit would go towards the loan. IF R = 100,000/2500 = 40 weeks Our weekly earning is $2500.00 we can then pay back the loan in 40 weeks. Table of Values 4. Fill in the missing values in the table below. Round dollar amounts to the nearest hundredth (cent). Weight of Laundry Machines Needed (M) Sales (s) Cost per load (c) Profit (P) sales=$12.00*M c=$0.97*M P=s-c P 10 lbs 1 $12.00 $0.97 $11.03 0 30 lbs 2 $24.00 $1.94 $22.06 $11.03 50 lbs 3 $36.00 $2.91 $33.09 $22.06 70 lbs 4 48.00 $3.88 $44.12 33.09 5. Provide two examples for the number of machines needed to wash a load over 100 pounds. (Choose any amount over 100 pounds in your examples; the amount does not matter as long as your math is correct.) Provide the profit for your choices. Show the formulas you used to determine the values. Machines needed to wash _300__ pounds: M=300/20 = M = 15 Machines needed to wash _400__ pounds: M=400/20= M=20 Profit from 110.30___ pounds: If S = 12*M (12*15) =S is $180.00, C= .97*M (.97*15) = C is $14.55 and P = s-c $120.00 - $14.55= $165.45 Profit from _220.70___ pounds: If S = 12*M (12*20)= S is 240.00 C=(.97*20)= C is $19.40 P=s-c (240.00-19.40) = 220.60 Profit =$220.70 6. What does the P value represent? The P value represents the change in profit from the previous value. 7. What does P equal for a change from four machines to two machines? The P is change from 4 machines to 2 machines is -$22.06 Machine 4 P = $11.03 Machines 3 P= $22.06 and Machine 2 P is $11.03 equal to $-22.06 Sales per Customer vs. Pounds of Laundry per Customer 8. What does the graph of \"Sales per Customer vs. Pounds of Laundry per Customer\" (above) show? The graph is depicting Sales per customer vs Pounds of laundry per customer it shows that if the punds of laundry needed increases the sales increases to. 9. Explain the meaning of the open and closed circles on the graph above. The open circle means that the value and or the number is not included and the closed circle means that and /or number is included. \"When graphing a linear inequality on a number line, use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to\" (Roberts, 2017, p1). 10. Explain why the graph above contains separate line segments. What does each break represent? The graph above contains separate line segment because it is based on pounds of laundry that is needs to be washer per customer. Because the customer is exceeding the most that is allowed which is 20 lbs. in washer #1 he or she now has to use a second washer for his additional clothes and will need to pay $12 for the loads ranging between 20-40lbs. The consumer is now responsible for 2 washers $12.00 *2=$24.00 The third break shows that the consumer has now exceeded the maximum allowed of 40lbs and will need to use another washer for the remaining laundry. Load over 40lbs the cost will be an additional $12.00. The user now will need to pay $24.00 + $12.00= 36.00 total 11. What is the slope of each line segment in the graph above? What does the slope mean? The slope of each line segment means that since all the lines are horizontal, and there is no steepness then the slope is equal to zero. When a slope is zero then there is no change in the amount of sale for each interval. 12. What is the domain and range of the graph above? Domain: x>0 Range: 12,24,36,48,60,72,84,96 The range is any multiple of 12. References: Roberts, D. (2017). Basic Linear Inequalities - MathBitsNotebook(A1 - CCSS Math). Mathbitsnotebook.com. Retrieved 6 August 2017, from https://mathbitsnotebook.com/Algebra1/Inequalities/IQRefresh.html