With this assignment, I am supposed to write a memo and a reasoning for each questions. I can do those parts. I would only like for a handwritten math solutions to be done.
Business Calculus Final Take Home Exam Summer 2020 Select 6 of the 7 problems to answer. For each problem that you solve (remember, pick 6), you are required to do two things: 1. Solve the problem and completely (and neatly) show all work. You must use tools you learned in this class to solve. 2. Type a memo to the manager (or whoever the problem says to write a memo to). In your memo you are to describe your recommendation and explain your reasoning. This is a professional memo. You must write using proper grammar, spelling and punctuation. The last page of this document contains a fairly standard memo template. 3. Upload two separate files to Canvas. One file contains all your memos and the other contains all you mathematical solutions (i.e., show all work). I recommend the following for each problem: First, identify the type of problem you are being asked to solve. Is it a constrained optimization problem requiring a Lagrangian setup? Would solving the problem requiring using a definite integral? Is the problem a straightforward optimization problem like maximizing profits or revenues, or minimizing costs? The first problem is simply interpretative; look at the graph and explain. The exam is open-book, open-note, and open-Internet, but you MUST show your work or steps. For example, if you choose to use Wolframalpha.com, then you must still show your work and explain your steps. Wolframalpha.com is simply a source for checking your work. Problem 1 It is the year 2020, and the world is experiencing a pandemic, COVID-19. You are a consultant working for the largest healthcare provider in the United States. [For example, Intermountain Healthcare is the largest healthcare provider in the intermountain west.] You have been hired to provide statistical updates to the healthcare provider regarding the spread of COVID-19. The provider simply wants you to provide some information about the growth of daily confirmed cases in the United States beginning back when we started to see our first cases. Take a look at the below graphic (and you can get a better view by going to the website link provided). Discuss the growth rate of cases and factors contributing to the increase beginning around the 100th day. You should do some research to help understand contributing factors. You can “smooth” out the curve to identify peaks and inflections. Go to the website for the below “interactive” graphic, https://ourworldindata.org/coronavirus/country/united-states?country=~USA https://ourworldindata.org/coronavirus/country/united-states?country=~USA Problem 2 You manage a local machine shop and the owner of the company would like to understand a typical worker’s productivity. You have modeled worker productivity for assembling components, N, after h consecutive hours as follows: ?(ℎ) = 100 1 + 10?−0.7ℎ To maintain worker productivity, after how many hours of consecutive working should workers be given a break? Explain why? When you respond to the owner, you should include a graphical representation of worker productivity. Also, compare the number of components produced in an 8 hour day with a break in the day versus when a worker works for a continuous 8 hours without a break. Problem 3 Aspire Cable Company actively promoted sales in a town that previously had no cable service. Once Aspire saturated the market, it introduced a new 50-channel system and raised rates. As the company began to offer its expanded system, a different company, BigSatellite Cable, began offering satellite service with more channels than Aspire and at a lower price. A model for Aspire’s revenue for the 26 weeks after it began its sales campaign is ?(?) = −3?4 + 160?3 − 3000?2 + 24000? dollars Where x is the number of weeks since Aspire began sales. The figure and table below represent some points for revenue. Weeks Revenue (dollars) 2 $37,232 6 $66,672 10 $70,000 14 $71,792 18 $78,192 22 $76,912 26 $37,232 For this problem, you should use calculus to find extremas. Calculus will “smooth” out the curve above by assuming a continuous relationship. Interpret the meaning of your analysis as it corresponds to the scenario presented above. Please report back to the Sale’s department about the performance of the campaign and when revenues peaked. Please explain when you believe BigSatellite Cable started to have a negative effect on Aspire’s sales. Problem 4 You are the manager of a manufacturing firm, and you are considering purchasing a new machine for your assembly-line process. The machine costs $105,000. The economists that work for the company estimate that the additional income from the machine will be a constant $7800 for the first year, then will increase by $700 each year after that. In order to buy the machine, the company needs to be convinced that it will pay for itself by the end of 8 years with this additional income. Money can earn 2.7% per year, compounded continuously. Should the company buy the machine? Please provide your analysis to the chief operating officer (COO) of the company. Problem 5 Your client has inherited a failing soda pop business from her recently deceased uncle. Your client is in the process of trying to overhaul the business. The first step is understanding the cost of making a batch of the soda pop. You have estimated the cost in dollars to produce a batch of the soda pop as ?(?, ?) = 2200 + 27?3 − 72?? + 8?2 Where x is the number of kilograms of sugar added to each batch and y is the number of grams of flavoring per batch. Please help your client identify the quantities of sugar and flavoring that minimize the cost of producing a batch of the soda pop. What is the minimum cost? After identifying the relationship between inputs and costs for your client, what would you advise as the next steps for assessing the business? Please advise your client. Problem 6 You are an economic advisor for the governor. You have been asked to measure the economic welfare of the market for a state-provided health insurance plan that would be made available to all citizens in the state. [Economic welfare is the sum of producer and consumer surplus]. Use the below estimated monthly demand and supply curves to find equilibrium price and quantity and economic welfare. You also need to provide a graphical representation (with actual values labeled) of supply and demand based on the estimated monthly demand and supply functions given below. ?(?) = ? = −0.4? + 23 ?(?) = ? = 0.03?2 + 3 The quantity of enrollees, q, is in thousands of citizens, and p is the monthly premium price that a enrollee in the plan would pay. Round q to the nearest whole number and equilibrium price, p¸ to the nearest cent. To find consumer surplus and producer surplus, you are REQUIRED to use a definite integral for each. Problem 7 You are a small business consultant, and your client will be starting a Beekeeping Store, which will provide all the materials needed for beekeepers (apiarists) as well as provide consulting advice to beekeepers. Your client read the following article on honey cohesiveness and would like you to help him understand the mathematics. Shinn, J. M., S. L. Wang. (1990). “Textural Analysis of Crystallized Honey Using Response Surface Methodology.” Canadian Institute of Food Science and Technology Journal 23(4-5): 178-182. From this paper, the cohesiveness of honey can be modeled by ?(?,?) = 106.35 − 3.7? − 4.7? + 0.04?2 + 0.08?2 + 0.06?? Where G is the percentage of glucose and maltose and M is the percentage of moisture. Things to consider in your response to your client are: 1. Find the absolute minimum cohesiveness of honey. 2. FDA requirements. The FDA restrictions for Grade A honey require that the combined percentages of glucose and maltose, and moisture not exceed 40%. Given this constraint, what is the minimum measure of cohesiveness that is possible? Memo To: From: Date: Re: Type your memo here.