This is the final assignment.

Everyone MUST pass this assignment with a B-(120 out of 150 points) to pass in this course.

Choose two of the following four scenarios, and write a 4-page essay

• 2 pages for each scenario.
• Essay must be typed.
• Font size: 12pt
• Double spaced with 1” margins
• Students MUST provide mathematical models in detail for each scenario to receive full credit and if necessary, you must provide the excel output using Excel Solver or Data Analysis in scenario 2, 3 or 4.
• Make sure biblical integration should be provided as well, meaning you should provide a biblical perspective in your essay.
• Late submissions will not be accepted.

Scenario 1

Suppose California Baptist University (CBU) is considering creating a brand new major, Medical Science, in 2016. If CBU sticks with its current curriculum and creates no further majors, then the annual revenue will be tuition ($11.5 million), donation ($4.4 million), and research grants ($2.5 million). At the same time, CBU incurs costs such as employee salaries ($6 million), rent ($5 million), and utilities ($2.2 million) to maintain its business annually. If CBU decides to create new majors, then there are three possibilities. First, if medical research proves to be successful, and new faculty members in medical science, receive funding more actively from the state and federal government, then annual research grants are expected to increase from $2.5 to $8 million. Also, medical research alumni are likely to donate funds to CBU in the future, which also is expected to increase the amount of donation from $4.4 to $6 million, so the total revenue would increase by $7.1 million. On the other hands, the university should hire more staff/faculties in those areas, which would increase employee salaries from $6 to $8 million, while rent and utilities stay the same as under “offering no new major” option. However, business analysts expect this probability to be 35%. Second, there is also a 40% chance that faculties in medical science have a hard time receiving federal research funds due to the recession, in which case, the research grants decreases from $2.5 to $0.7 million, while revenues from tuition and donation stay the same as under “offering no new major” option. In this scenario, CBU will still have to pay employment salary ($8 million) and rent and utilities stay the same as under “offering no new major” option. Finally, uncertain economic or regional factors may lead to a huge drop in enrollment, decreasing tuition revenue. The boom in the housing market and recent drought increases rent and utilities dramatically. In other words, there is a 25% chance that CBU is suffering a loss of $3.5 million (net profits), if it chooses to offer a new major.

Question: Make a recommendation regarding whether CBU should offer a new major or stick to its current curriculum, using a decision tree (Hint: You MUST calculate the expected net profit of the option “offering a new major” and compare it to the net profit of the option of “offering no new major”)

Please refer to the attached document #1 Guideline.ppsm for scenario 1.

Scenario 2

California Pacific is a lumber company that has three sources of wood and five markets to be supplied. The annual availability of wood at sources 1, 2, and 3 is 15, 20, and 15 million board feet, respectively. The amount that can be sold annually at markets 1, 2, 3, and 4 and 5 is 11, 12, 9, 10 and 8 million board feet, respectively.

In the past, the company has shipped the wood by train. However, because shipping costs have been increasing, the alternative of using ships to make some of the deliveries is being investigated. This alternative would require the company to invest in some ships. Except for these investment costs, the shipping costs in thousands of dollars per million board feet by rail and by water (when feasible) would be the following for each route.

The capital investment (in thousands of dollars) in ships required for each million board feet to be transported annually by ship along each route is given next.

Considering the expected useful life of the ships and the time value of money, the equivalent uniform annual cost of these investments is one-tenth the amount given in the table. The objective is to determine the overall shipping plan that minimizes the total equivalent uniform annual cost (including shipping costs).

You are the head of the management science team that has been assigned the task of determining this shipping plan for each of the three options listed next.

Option 1: Continue shipping exclusively by rail

Option 2: Switch to shipping exclusively by water (except where only rail is feasible)

Present your results for each option and compare.

Scenario 3

The vintage restaurant, on Captiva Island near Fort Myers, Florida, is owned and operated by Karen Payne. The restaurant just completed its third year of operation. During that time, Karen sought to establish a reputation for the restaurant as a high-quality dining establishment that specializes in fresh seafood. Through the efforts of Karen and her staff, her restaurant has become one of the best and fastest-growing restaurants on the island. To better plan for future growth of the restaurant, Karen needs to develop a system that will enable her to forecast food and beverage sales by month for up to one year in advance. Table 1 shows the value of food and beverage sales ($1000s) for the first three years of operation

Table 1- Food and Beverage Sales for the Vintage Restaurant ($1,000s)

Perform an analysis of the sales data for the vintage restaurant. Prepare a report for Karen that summarizes your findings, forecasts, and recommendations, including the following:

• Construct a time series plot.
• Comment on the underlying pattern in the time series.
• Using the quarterly dummy variable approach, forecast sales for January through December of the fourth year. For instance, you would have three dummy variables – quarter 1, quarter 2, and quarter 3 and quarter 4 is a baseline quarter. Quarter 1=1 if sales occurs in January, February, or March, otherwise, Quarter 1=0. Quarter 2=1 if sales occurs in April, May or June, otherwise, Quarter 2=0. Quarter 3=1 if sales occurs in July, August, or September, otherwise, Quarter 3=0.
• Assume that January sales for the fourth year turn out to be $295,000. What was your forecast error? If this error is large, Karen may be puzzled about the difference between your forecast and the actual sales value. What can you do to resolve her uncertainty in the forecasting procedure?

Scenario 4

Better Fitness, Inc. (BFI), manufactures exercise equipment at its plant in Freeport, Long Island. It recently designed two universal weight machines for the home exercise market. Both machines use BFI-patented technology that provides the user with an extremely wide range of motion capability for each type of exercise performed. Until now, such capabilities have been available only on expensive weight machines used primarily by physical therapists. At a recent trade show, demonstrations of the machines resulted in significant dealer interest. In fact, the number of orders that BFI received at the trade show far exceeded its manufacturing capabilities for the current production period. As a result, management decided to begin production of the two machines. The two machines, which BFI named the BodyPlus 100 and the BodyPlus 200, require different amounts of resources to produce.

The BodyPlus 100 consists of a frame unit, a press station, and a pec-dec station. Each frame produced uses 4 hours of machining and welding time and 2 hours of painting and finishing time. Each press station requires 2 hours of machining and welding time and 1 hour of painting and finishing time, and each pec-dec station uses 2 hours of machining and welding time and 2 hours of painting and finishing time. In addition, 2 hours are spent assembling, testing, and packaging each BodyPlus 100.

The BodyPlus 200 consists of a frame unit, a press station, a pec-dec station, and a leg- press station. Each frame produced uses 5 hours of machining and welding time and 4 hours of painting and finishing time. Each press station requires 3 hours of machining and welding time and 2 hours of painting and finishing time, each pec-dec station uses 2 hours of machining and welding time and 2 hours of painting and finishing time, and each leg-press station requires 2 hours of machining and welding time and 2 hours of painting and finishing time. In addition, 2 hours are spent assembling, testing, and packaging each BodyPlus 200.

For the next production period, management estimates that 500 hours of machining and welding time; 350 hours of painting and finishing time; and 120 hours of assembly, testing, and packaging time will be available.

The net retail price of the BodyPlus 100 and the BodyPlus 200 are $350 and $445, respectively. Although some flexibility may be available to BFI because of the unique capabilities of the new machines. Authorized BFI dealers can purchase machines for 70% of the suggested retail price. BFI’s president believes that the unique capabilities of the BodyPlus 200 can help position BFI as one of the leaders in high-end exercise equipment. Consequently, she states that the number of units of the BodyPlus 200 produced must be at least 35% of the total production of BodyPlus 100.

Analyze the production problem at Better Fitness, Inc., and prepare a report for BFI’s president presenting your findings and recommendations. The report should include the following items:

• The recommended number of BodyPlus 100 and BodyPlus 200 machines (In other words, find the optimal level of production for BodyPlus 100 and BodyPlus 200 using linear programming model).
  • Objective function: Total profit
  • BodyPlus 200 requirement constraint
  • Non-negativity constraint
  • Time Constraint:
    • Machining & Welding
    • Painting & Finishing
    • Assembly, Test, and Packaging
• The effect on profits of the requirement that the number of units of the BodyPlus 200 produced must be at least 25% of the total production of BodyPlus 100. where efforts should be expended in order to increase contribution to profits
• Include a copy of your linear programming model