per cap sold. In addition, Riya believes that each cap will use about $2.50 worth of supplies (including thread, replacement of sewing needles, machine maintenance, etc.). Finally, Made to Or- der Caps, Inc., requires that each franchisee spend $250 per month on leaflets and brochures to advertise the product. Riya is considering a business venture - selling custom embroi- dered baseball caps from a pushcart kiosk at College Mall. The caps will be available in 12 different colors and one-size fits all. The caps' unique feature is that almost any name, phrase, or logo, can be stitched onto the cap while the customer waits. Thus, a customer can obtain a cap with his or her own name, monogram, special saying or favorite logo in a wide variety of thread colors, sizes and fonts. Based on preliminary market research and input from the franchising company, Riya plans on selling each embroi- dered cap for $20. Riya plans to acquire the necessary technology (two indus- trial strength sewing machines hooked up to PCs with scanners and all of the necessary software) by obtaining a franchise from Made to Order Caps, Inc. Made to Order Caps, Inc., sells all of the necessary equipment and technology and provides the inventory of caps and other supplies. In addition, Made to Order Caps, Inc., trains prospective franchises such as Riya in the basics of running the business and operating the machines. Riya will need to buy the caps from Made to Order Caps, Inc. for $4 per cap and pay a royalty to the franchising company of $2 Riya discovers that College Mall would supply her with the pushcart and all of the necessary equipment for proper display. The license from the mall also allows Riya to use electricity con- sumption, but she will have to obtain two business telephone lines at a cost of $50 per line per month. College Mall is willing to license the space and equipment at a monthly price of $1,970 without any long-term commitments. To generate maximum sales, Riya wants to keep the push- cart open for business from 10 A.M to 10 P.M. Monday through Friday, and from 10 A.M. to 6 P.M. on Saturday and Sunday. Riya is willing to put in 50 hours at the kiosk, and she can obtain addi- tional part-time help at $10 per hour (only one individual is re- quired to operate the business). Riya's only other significant ex- pense is setting up to accept credit cards. Riya anticipates that 75% of her sales will be credit card sales and the credit card com- pany charges Jessica a fee of 2% of the selling price. Riya is wondering whether she can make money out of this business. You should come up with an analysis (For the purpose of the analysis, assume that each month has exactly 4 weeks) that should help Riya in deciding whether this is a worthy venture. Your analysis should include key numbers such as how many caps should Riya sell (and how much revenue she should generate) per month in order to make sure that she at least breaks even. You should include a mathematical expression for expected profit per month in your analysis. selling price. She is determined to use all that she learned in her economics class to figure out the optimal selling price for her product. After conducting a market research study with Jessi's help, Riya comes up with the following prediction for the baseball cap's monthly demand: Price per cap Demand $20 300 25 250 28 220 30 200 32 180 34 160 1)How does this price information affect your earlier characteriza- tion of mathematical expression for profit equation? 2) Recommend the optimal price for Riya. Justify your answer. Is there any reason to suspect the existence of multiple optimal prices? Why or why not? 3) Finally, what do you think about Riya's aspiration for a monthly profit of $4,032 and Jessi's estimated volume of business of 1,000 caps per month? Riya's best friend Jessi plans to help Riya as her part time helper in this business. Jessi thinks that Riya will be able to sell 1,000 caps per month. However, Jessi's aspiration is to earn a net- profit of $4,032 per month before taxes. Your analysis should characterize the risk characteristics of these two business scenar- ios quantitatively, assuming that they manage to achieve these targets. Riya earned an "A+" in microeconomics last semester and she is aware of the inverse relationship between demand and equip- ddition characteriz that they n | Price per cap Demand $20 300 250 220 all 200 180 let he in the mall 160