This part of assessment is targeted at the following learning outcomes of the course -
- Analyse the limitations of rational decision making in organisational environments and relate to real world contexts.
- Advise on and manage the implementation of organisational decisions.
Task: Discussion and Numerical Questions on decision making
1. Discussion Question
Managers are quick to claim that quantitative analysts talk to them in a jargon that does not sound like English. List FOUR terms from Chapter 1 of the text book (Quantitative Analysis for Management, Render et al.) that might not be understood by a Manager. Then EXPLAIN in non-technical terms what each of FOUR terms means with suitable example where needed.
2. Numerical Questions
Please read "Chapter 7: Linear Programming Models" of the textbook and then answer the following decision-making questions based on LP model as required.
Q1. The Electrocomp Corporation manufactures two electrical products: air conditioners and large fans. The assembly process for each is similar in that both require a certain amount of wiring and drilling. Each air conditioner takes 3 hours of wiring and 2 hours of drilling. Each fan must go through 2 hours of wiring and 1 hour of drilling. During the next production period, 240 hours of wiring time are available and up to 140 hours of drilling time may be used. Each air conditioner sold yields a profit of $25. Each fan assembled may be sold for a $15 profit. Formulate and solve this LP production mix situation to find the best combination of air conditioners and fans that yields the highest profit. Use the caner point graphical approach.
Q2. Electrocomp's management realizes that it forgot to include two critical constraints (see Question 1). In particular, management decides that there should be a minimum number of air conditioners produced in order to fulfill a contract. Also, due to an oversupply of fans in the preceding period, a limit should be placed on the total number of fans produced.
(a) If Electrocomp decides that at least 20 air conditioners should be produced but no more than 80 fans should be produced. What would be the optimal solution? How much slack is there for each of the four constraints?
(b) If electrocomp decides that at least 30 air conditioners should be produced but no more than 80 fans should be produced, what would be the optimal solution? How much slack is there for each of the four constraints at the optimal solution?
Q3. Bhavika Investments, a group of financial advisors and retirement planners, has been requested to provide advice on how to invest $200,000 for one of its clients. The client has stipulated that the money must be put into either a stock fund or a money market fund, and the annual return should be at least $14,000. Other conditions related to risk have also been specified, and the following linear program was developed to help with this investment decision:
Minimize risk = 12 S + 5M
subject to
S + M = 200,000 total investment is $200,000
0.10S + 0.05M ≥ 14,000 return must be at least $14,000
M ≥ 40,000 at least $40,000 must be in money market fund
S, M ≥ 0
where
S = dollars invested in stock fund
M = dollars invested in money market fund
The QM for Windows output is shown below.
(a) How much money should be invested in the money market fund and the stock fund? 'What is the total risk?
(b) What is the total return? What rate of return is this?
(c) Would the solution change if risk measure for each dollar in the stock fund were 14 instead of 12?
(d) For each additional dollar that is available. How much does the risk change?
(e) Would the solution change if the amount that must be invested in the money market fund were changed from $40,000 to $50.000?
