The owners of Riverside Cycle in Haverhill are concerned that they are not maximizing their profits. They wish to determine the profit-maximizing level of sales for their shop. The following monthly data represents the number of bicycles produced and sold, total cost of production, and total revenue. All are in US dollars.

a) Extend the table and calculate the profit for the number of bicycles that is listed above. Provide the new, extended table with your answers. What is the profit-maximizing value of sales? b) Using MSExcel, MSWord, or some online graphing tool, create a scatterplot of x versus C and a separate scatterplot of x versus R. Treat the number of bicycles, x, as the independent variable. Be sure to title and label each graph. c) To estimate the revenue function R(x), use a graphing calculator to find the quadratic function of best fit, treating total revenue as the dependent variable and number of bicycles x as the independent variable. Round each value to 4 decimal places. d) To estimate the cost function C(x), use a graphing calculator to find the cubic function of best fit, treating total cost as the dependent variable and number of bicycles x as the independent variable. Round each value to 4 decimal places. e) Find the profit function, P(x), using R(x) and C(x) from parts c and d. Round each value to 4 decimal places. f) Graph the function P(x) using MSExcel, MSWord, or some online graphing tool. Using the MAXIMUM feature of your graphing calculator, determine the profit-maximizing value of the P(x) function. How many bicycles should they sell and what is the maximum profit?

Total Revenue, R Number of Bicycles, x 0 25 60 102 150 190 223 249 Total Cost of Production, 24,000 27,750 31,500 35,250 39,000 42,750 46,500 50,250 0 28,000 45,000 53,400 59,100 62,360 61,485 59,875 Total Revenue, R Number of Bicycles, x 0 25 60 102 150 190 223 249 Total Cost of Production, 24,000 27,750 31,500 35,250 39,000 42,750 46,500 50,250 0 28,000 45,000 53,400 59,100 62,360 61,485 59,875