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The Kigawa Corporation manufactures two electrical products: air Conditioners and large fans.
1. The Kigawa 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, drilling, taper-turning and grinding operations.
Each air conditioner takes 5 hours of wiring, 3 hours of drilling, 2 hours of taper-turning and 0.25 hours of grinding operations. Each fan must go through 6 hours of wiring, 4.5 hours of drilling, 1 hour of taper-turning and 0.35 hours of grinding operations. During the next production period, 540 hours of wiring time, 380 hours of drilling time, 200 hours of taper-turning time are available and up to 80 hours of grinding time may be used.
Each air conditioner is sold at a price of R550. Each fan assembled is sold at a price of R610. The labour wage per hour for the aforementioned operations is R50 each. Kigawa Corporation decides that at least 45 air conditioners should be produced but no more than 100 fans should be produced.
1.1 Formulate a Linear Programming (LP) model that will maximize the profit of Kigawa Corporation.
1.2 Solve this LP using the graphical method.
1.3 Determine the slack or surplus value for each of the constraints?
2. Market Researchers Inc has hired a project consulting firm to perform a study to determine if a project to be embarked by this company will be successful or it will fail. In similar studies performed by past Market Researchers Inc, whenever the project was actually successful, the market research study indicated that the project will be successful 85% of the time. On the other hand, whenever the project actually fails, the market study incorrectly predicted that the project will be successful; 20% of the time. Before the study is performed, it believed there is 70% chance that the project will be successful. When Market Researches Inc performs the study for this project the results predicts it will be successful.
2.1. Given the results of this study, what is the probability that the project will actually be successful?
2.2. Given the results of this study, what is the probability that the project will actually fail?
2.3. If the Market Researchers, Inc. predicts that the project will fail, what is the probability that the project will actually be successful?
3. Trowbridge Manufacturing produces cases for personal computers and other electronic equipment. The quality control inspector for this company believes that a particular process is out, of control. Normally, only 15% of all cases are deemed defective due to discolorations. If 8 such cases are sampled:
3.1. What is the probability that there will be 2 defective cases, if the process is operating correctly?
3.2. What is the probability that there will be exactly 4 defective cases?
The time to finish a construction project is normally distributed with a mean of 80 weeks and a variance of 64 weeks.
3.3. What is the probability that the project will be finished in 85 weeks or less?
3.4. What is the probability that the project will take longer than 90 weeks?
3.5. What is the probability that the project will be done newtwwen 87 weeks and 90 weeks?
4. Mr Kagiso, a project manager is not sure what he should do. He can either build a quaduplex (i.e. a building with four apartments), build a duplex, gather additional information, or simply do nothing. If he gathers additional information, the results could be either favourable or unfavourable, but it would cost him R6500 to gather the information. Kagiso believes that there is a 78% chance that the information will be favourable. If the rental market is favourable, Kagiso will earn R35000 with the quaduplex or R10000 with the duplex.
Kagiso doesn't have the financial resources to do both. With an unfavorable rental market however, Kagiso could lose R15000 with the quadplex or R7500 with the duplex. Without gathering additional information, Kagiso estimates that the probability of a favourable market is 0.85. A favourable report from the study would increase the probability of a favourable rental market to 0.90. Furthermore, an unfavourable report from the additional information would decrease the probability of a favourable rental market to 0.3. Of course, Kagiso could forget all of these numbers and do nothing.
What is your advice to Kagiso as a decision analyst?
