Both manufacturing lines are operating for one 8-hour shift per day. The goal is to analyze Digital Imaging’s production and determine the optimal quantity of each printer to manufacture. A report will be prepared for Dell’s president, presenting the findings and recommendations. Factors to consider include: 1. The recommended quantity of each printer to maximize profit contribution during an 8-hour shift. Reasons for management’s potential hesitance to implement the recommendation should be explored. 2. Additionally, management has stated concerns with the number of units produced.
In order to maximize profit during an 8-hour shift, it is crucial to produce an equal or greater quantity of ODL-91 0 printers compared to the number of ODL-950 units. The question at hand is: How many units of each printer should be manufactured?
Furthermore, we must assess whether the solution devised in the previous section effectively balances the total time spent on line 1 and line 2. This allocation of time may raise concerns for management.
Lastly, management has expressed a desire to expand the model in order to achieve a more optimal equilibrium between the total time allocated for line 1 and line 2.
Management has a goal of limiting the time difference between line 1 and line 2 to 30 minutes or less, while maximizing profit contribution. They want to determine the quantity of each printer that should be produced in order to achieve this goal. Additionally, they are interested in understanding how this workload balancing will impact the total profit in part (2).
In part (1), if management’s objective is to maximize the total number of printers produced per shift rather than total profit contribution, they would like to know how many units of each printer should be produced per shift.
What impact does this goal have on overall profits and workload distribution? Include a linear programming model and graphical solution for each solution developed in the appendix of your report. Case Problem 3 PRODUCTION STRATEGY Better Fitness, Inc. (FBI) produces exercise equipment at its Freeport, Long Island plant. It has recently created two universal weight machines for the home exercise market. These machines utilize FBI-patented technology that enables users to perform a wide range of exercises with exceptional motion capability for each.
Previously, these capabilities were only found on expensive weight machines mainly used by physical therapists. However, at a recent trade show, the machines were demonstrated and garnered significant interest from dealers. In fact, the number of orders received by FBI at the trade show exceeded their current manufacturing capabilities. Consequently, the management made the decision to commence production of two machines. These machines, known as the Body’s 100 and the Body’s 200, require varying amounts of resources for production. The Body’s 100 comprises a frame unit, a press station, and a peck-DCE station.
Each frame produced requires a total of 6 hours, consisting of 4 hours of machining and welding and 2 hours of painting and finishing. Similarly, each press station takes 3 hours, with 2 hours dedicated to machining and welding and 1 hour for painting and finishing. For each peck-DCE station, the time required is 4 hours – 2 hours for machining and welding and 2 hours for painting and finishing. Additionally, each Body’s 100 product undergoes a 2-hour process of assembling, testing, and packaging.
The material costs are $450 for each frame, $300 for each press station, and $250 for each peck-DCE station. Furthermore, packaging costs are estimated at $50 per unit.
The Body’s 200 consists of multiple stations: a frame unit, a press station, a peck-DCE station, and a leg press station. Machining and welding time for each frame is 5 hours, while painting and finishing time is 4 hours. The press station requires 3 hours of machining and welding time and 2 hours of painting and finishing time. Similarly, the peck-DCE station needs 2 hours of machining and welding time along with 2 hours of painting and finishing time. The leg press station also requires 2 hours of machining and welding time as well as 2 hours of painting and finishing time. Additionally, it takes another two hour to assemble, test, and package each Body-Plus 200.
The cost of raw materials for each frame is $650, for each press station is $400, for each peck-DCE station is $250, and for each leg-press station is $200. The estimated snacking costs per unit are $75. The available time for the next production period includes 600 hours for machining and welding, 450 hours for painting and finishing, and 140 hours for assembly, testing, and packaging. Currently, labor costs are $20 per hour for machining and welding, $15 per hour for painting and finishing, and $12 per hour for assembly, testing, and packaging.
The Body’s 100 is priced at $2400, while the Body’s 200 has a price tag of $3500. However, pricing for FBI may vary due to the unique capabilities of these new machines. Authorized FBI dealers have the opportunity to purchase these machines at a discount of 70% off the suggested retail price. The president of Bi believes that by emphasizing the distinctive features of the Body’s 200, FBI can establish itself as a leading provider of high-end exercise equipment. Therefore, it is recommended that at least 25% of total production consists of units from the Body Plus 200.
Managerial Report Analyze the production problem at Better Fitness, Inc., and prepare a report for Bi’s president presenting your findings and recommendations. Include (but do not limit your discussion to) a consideration of the following items:
1. What is the recommended number of Body’s 100 and Bodies 200 machines to produce?
2. How does the requirement that the number of units of the Body’s 200 produced be at least 25% of the total production affect profits?
3. Where should efforts be expended in order to increase profits?
Include a copy of your linear programming model and graphical solution in an appendix to your report.
Case Problem 4 HART VENTURE CAPITAL
Hart Venture Capital (HAVE) specializes in venture capital for software development and Internet applications. HAVE currently has two investment opportunities: (1) Security Systems, a firm requiring additional capital to develop an Internet security software package; and (2) Market Analysis, a market research company requiring extra capital to develop a software package for customer satisfaction surveys. In exchange for Security Systems stock, the firm has asked for $600,000 in year 1, $600,000 in year 2, and $250,000 in year 3 over the next three years.
Market Analysis has requested that HAVE provide $500,000 in the first year, $350,000 in the second year, and $400,000 in the third year within a three-year timeframe
HAVE believes both investment opportunities are worth pursuing but is only willing to allocate a maximum of $800,000 for both projects in the initial year,
a maximum of $700,000 in the second year,
and $500,000 in the third year due to other investments
HVAC’s financial analysis team advises maximizing
the net present value of Security Systems and Market Analysis combined investment.
The net present value (NPV) takes into account the projected value of the stock after three years and the required capital outflows in each year. HVAC’s financial analysis team estimates that fully funding the Security Systems project has an NPV of $X, while fully funding the Market Analysis project has an NPV of $1. HAVE has the option to fund any percentage of both projects.
For instance, if HAVE chooses to finance the security systems project, it would necessitate investments of $240,000 in year 1, $240,000 in year 2, and $100,000 in year 3. In this particular situation, the net present value of the Security Systems project would be 0.40 ($1 = $720,000). The calculation of investment amounts and net present value for partially funding the Market Analysis project would follow a similar approach. A managerial report should be compiled that examines HVAC’s investment predicament and provides a presentation of findings and recommendations.
Include (but do not limit your discussion to) a consideration of the following items:
1. What is the recommended percentage of each project that HAVE should fund and the net present value of the total investment?
2. What capital allocation plan for Security Systems and Market Analysis for the coming three-year period and the total HAVE investment each year would you recommend?
3. What effect, if any, would HVAC’s willingness to commit an additional $100,000 during the first year have on the recommended percentage of each project that HAVE should fund? What would the capital allocation plan look like if an additional $100,000 is made available?
5. What is your recommendation as to whether HAVE should commit the additional $100,000 in the first year? Provide model details and relevant computer output in a report appendix.
Sensitivity Analysis Case Problem 5 INVESTMENT STRATEGY J. D. Williams, Inc., is an investment advisory firm that manages more than $120 million in funds for its numerous clients. The company uses an asset allocation model that recommends the portion of each client’s portfolio to be invested in a growth stock fund, an income fund, and a money market fund.
The firm has established limitations on fund allocation to promote variety in client portfolios. These guidelines state that the growth fund should not surpass 40% of the overall portfolio value. Furthermore, the income fund should represent between 20% and 50% of the total, while at least 30% must be invested in the money market fund.
Furthermore, the company’s goal is to assess each client’s risk tolerance and personalize their portfolio accordingly. For instance, Williams recently acquired a new client with an investment capacity of $800,000. After evaluating the client’s risk tolerance, Williams set a maximum risk index of 0.05 specifically for this client. The firm’s risk indicators indicate that the growth fund poses a risk level of 0.10, the income fund carries a risk level of 0.07, and the money market fund has a risk level of 0.01.
The overall risk index of the portfolio is determined by calculating a weighted average of the risk rating for the three funds. The weights used in this calculation represent the fractions of the client’s portfolio invested in each fund. Additionally, Williams has estimated that the growth fund will yield 18% annually, the income fund will yield 12.5%, and the money market fund will yield 7.5%. Based on this information, it is necessary to advise the new client on how to allocate their $800,000 among these three funds. Developing a linear programming model is essential to achieve maximum yield for the portfolio.
Use your model to develop a managerial report. Managerial Report 1. Recommend the distribution of the $800,000 among the three funds. What is the expected annual yield for this investment recommendation? 2. Assuming an increased risk index of 0.055, how much would the yield increase and how would the investment recommendation change? 3. Returning to the original scenario with a risk index of 0.05, how would the investment recommendation change if the growth fund’s annual yield were revised downward to 16% or even to 14%? Additionally, what modifications would be made if the amount invested in the growth fund cannot exceed that in the income fund, based on client concerns about excessive allocation to the growth fund? 5. Your asset allocation model could be utilized to adjust portfolios for all firm clients when there are periodic revisions to the anticipated yields of the three funds. Do you recommend using this model?
