BUS107: Sports Fashion produces four types of protective jackets for sports enthusiasts: J1, J2, J3, and J4: Quantitative Methods Assignment, SUSS, Singapore

• Sports Fashion produces four types of protective jackets for sports enthusiasts: J1, J2, J3, and J4. Each J1 requires 4 minutes of machine time, 40 minutes of labor, and 3 units of protective shell materials. Each J2 requires 6 minutes of machine time, 90 minutes of labor, and 5 units of protective shell materials.

J3 and J4 are their premium models which they purchase semi-finished jackets from a contractor in Italy. J3 and J4 both require 8 minutes of machine time and 50 minutes of labor each. Each J3 and J4 only requires 1 unit of protective shell materials to complete its production.

1. The markup percentages (markup percentage = (unit profit)  (unit cost) × 100%) for J1 and J2 are set at 20%, while those for J3 and J4 are set at 28%. Maximizing profit is the main priority.
2. Based on the past sales data, combined demand for J3 and J4 is not more than
   30% of the combined sales for J1 and J2. Thus, the production ratio for J3 and
   J4 should also be kept to not more than 30% of the combined production for J1 and J2.
3. J2 is a popular jacket and its production should be at least twice as many as J1.
4. There are 40 machining hours and 300 labor hours available per week.
5. There are 1,000 units of protective shell materials available per week.
6. The weekly production budget is set at $5,000.

• Evergreen Technology is exploring the possibility of acquiring a 100% stake in a privately-owned start-up, AlphaTech, which is at the forefront of the next-generation communication chip for $10 million.

AlphaTech currently is in the final development stage of its flagship communication chip, Signale. The quality of the chip is measured by its latency level: Ultra-Low, Low, and Medium. If the chip could achieve Ultra-Low latency, AlphaTech’s valuation will increase to $100 million.

If the chip could achieve Low or Medium, AlphaTech’s valuation will be $50 million and $20 million, respectively. There could also be a possibility that the chip would fail to achieve latency level and not be viable to be commercialized. The followings are the probabilities for the eventual latency performance of the SignalOne chip:

Ultra-Low ~ 0.10
Low ~ 0.20
Medium ~ 0.40
Not viable ~ 0.30

Alternatively, Evergreen Technology could acquire a 40% stake in AlphaTech at the initial phase for $6 million while it waits for the preliminary test report on a SignalOne prototype. The preliminary test report can be positive or negative, and the probability of each is 0.5.

If the preliminary test report is positive, Evergreen Technology will then proceed to acquire the remaining 60% stake for $15 million. Given the positive preliminary test result, the probabilities for the eventual latency performance of the SignalOne chip will be:

Ultra-Low ~ 0.25
Low ~ 0.35
Medium ~ 0.30
Not viable ~ 0.10

In the event that the preliminary test report is negative, Evergreen Technology will either sell off its 40% stake at $5 million or proceed to acquire the remaining 60% stake for $3 million. Given the preliminary test result is negative, the probabilities for the eventual latency performance of the SignalOne chip will be:

Ultra-Low ~ 0.01
Low ~ 0.05
Medium ~ 0.20
Not viable ~ 0.74