Application Assignment 1 Math 1395 Business Math, Fall 2016 Overview The management of Bear Events, an event planning and promotions company, must decide between two venues for the upcoming Fall Benefit Concert. They have consulted us to assist the company in the decision analysis. Their research department has provided the necessary information to conduct the analysis. You should work in a team with up to 4 members, each bringing their own individual strengths to the group. A technical worksheet has is available in MML to document your final answers. Include your work, neatly hand-written and clearly labeled, on a separate page (20 points). You must use algebra to solve the problems (not graphing calculator features). To best maintain accuracy, round only your final answers. Simplify completely and round as appropriate. Research Provided The client's research department has provided the following estimates. A demand of 835 concert tickets can be expected at a price of $45 each. A demand of 707 concert tickets can be expected at a price of $69 each. Venue 1 has a fixed cost of $8,500 and a marginal cost of $30 for each ticket sold. Venue 2 has a fixed cost of $18,900 and a marginal cost of $13 for each ticket sold. To justify company resources and to ensure the even will benefit the charity, the CEO insists the tickets be sold for no less than $40 each. In appreciation of your work, Bear Events will collect donations to provide additional support for the fundraiser. Studies estimate that 25% of those who attend will give $5, 15% will give $10, and 2% will give $20. Analysis Each team should perform the following analysis. (Items 1-8 are 6 points each) 1. On average, how much should you expect to receive as an additional donation from each person attending the concert? (weighted average) 2. Assume the price-demand function is linear. Use the research department's estimates to find the relationship between the price p, and the number of concert tickets demanded, x. Find the relevant domain by considering realistic limitations on number of concert tickets and on price. Sketch the graph on your work page. 3. Find the revenue function, R(x), in terms of the number of concert tickets x. Find the relevant domain by considering realistic limitations on number of concert tickets and on price. Sketch the graph on your work page. 4. Assume the cost function is linear and use the research department's estimates to find the cost function for each of the two possible venues in terms of the number of concert tickets x. 5. Determine the minimum break-even quantity for each of the two possible venues. 6. Find the Profit function, P(x), for each of the two possible venues in terms of the number of concert tickets x. 7. a) Researcher Albert projects that there will be a demand of 700 concert tickets. If he is correct, which venue should management choose in order to earn the most profit? b) Based on his projections, Researcher Brandon proposes that the concert tickets should be priced high at $150, lowering the demand to only 275 concert tickets. In this case, which venue should management choose in order to earn the most profit? 8. Determine the maximum profit realized if Bear Events uses Venue 2. What is the average cost per ticket when this occurs? 9. Overall recommendation for Bear Events: Which venue should they use in order to obtain the most profit? What profit can be expected? How many concert tickets should they expect to sell in order to obtain that profit? At what price should concert tickets be sold to meet this demand? In addition to answering these questions, further analysis may be used to develop a well-supported recommendation. Support all calculations on the work page. (12 points) 10. Final report. Write a short proposal to Bear Events' board members describing your recommendations in question #9. This should be about one-half to one page, double-spaced. Include any information that you feel relevant. Use technology such as MS Excel to create one or two graphs displaying the important functions that could be used to help explain your recommendation to the board members. Note that to best compare items, multiple functions should be on the same axis. Be sure all necessary titles and labels appear on the graph, as you will not be there to explain the graph to the board. Be professional! 20 points. What to turn in Technical Worksheet (submit online) 60 points. After working as a team, each individual must submit answers in MyMathLab/Quizzes. Everyone is allowed two attempts. Make teamwork work to your advantage! Work page 20 points. This can be hand-written, but must be very neat, organized and labeled. You may need to rewrite a final copy, especially if you've corrected mistakes along the way. If the instructor cannot find a problem quickly or cannot easily read it, no points will be given. Show enough work that a good algebra student could follow the process - label functions. Don't forget to sketch two graphs. Turn in one per group. Individual grades will be penalized if Technical Worksheet is not complete. In other words, if you don't do your part to submit your answers online, you will not get your group's points for this work either. Final Report 20 points. Written proposal and graphics as described in question 10. Turn in one per group. Individual grades will be penalized if Technical Worksheet is not complete. In other words, if you don't do your part to submit your answers online, you will not get your group's points for this work either. There is a total of 100 points possible. This assignment is approximately 3% of the course grade. Your papers should look neat and professional - sloppy work will not receive full credit (print a new copy if needed). Please staple all pages of the group work together. Turn in your work before class begins on the due date. Late work may be penalized 20%. It is recommended that several team members have a copy of the work. REFER TO CLASS NOTES AND THE BOOK FIRST, THEN ASK YOUR INSTRUCTOR IF YOU STILL HAVE QUESTIONS. An instructor consultation is strongly recommended before turning in the final results. Available in MML/Document Sharing/Unit 1 Technical Worksheet 1395.a1.f16 1) On average, $_____________ per person is expected. 2) The linear price-demand function is p = D(x) = ___________________________, domain: ______ x _________. 3) The revenue function is R(x) = ________________________________, domain: ______ x _________. 4) The cost functions for each of the two possible venues in terms of x are C1(x) = ________________________________________________ and C2(x) = ________________________________________________. 5) Venue 1 will break even at a minimum of ___________ concert tickets. SUBMIT ANSWERS ONLINE: MyMathLab Venue 2 will break even at a minimum of ___________ concert tickets. 6) The profit functions for each of the possible Venues in terms of x are P1(x) = ________________________________________________ and P2(x) = ________________________________________________. 7) Using Researcher Albert's projections, Bear Events should choose Venue # ______ . The profit using Venue 1 is $__________________. The profit using Venue 2 is $____________________. Using Researcher Brandon proposal, Bear Events should choose Venue # ______ . The profit using Venue 1 is $__________________. The profit using Venue 2 is $____________________. 8) The maximum profit using Venue 2 is $_____________. The average cost per ticket is $_______________. 9) Overall recommendation for Bear Events' management: Recommended Venue: _______________ Max profit: $__________________ Number of concert tickets: ______________ Selling Price: $_________________ \f\f