Okyena Nti University is trying to decide whether or not to advertise its new one-year MSC degree programme. The number of students starting the programme is dependent on economic conditions. Required: Demonstrate, using a decision tree, whether the programme should be advertised.

• If economic conditions are poor (60% chance), 40 students are attracted.
  • Profit for 40 students = GH¢115,000.
  • Expected profit (poor conditions) = $0.60 \times 115,000 = 69,000$.
• If economic conditions are good (40% chance), 20 students are attracted.
  • Profit for 20 students = GH¢15,000.
  • Expected profit (good conditions) = $0.40 \times 15,000 = 6,000$.

The total expected profit if the programme is not advertised is:

$$\text{Expected Profit (No Advertising)} = 69,000 + 6,000 = \text{GH¢}75,000$$

The cost of advertising is GH¢15,000. This cost must be deducted from the profit for each outcome.

• Scenario A: Economic conditions are poor (60% chance).

  • There is a 65% chance advertising stimulates demand, increasing students to 50.
    • Profit for 50 students = GH¢165,000.
    • Net profit = $165,000 - 15,000 = 150,000$.
    • Probability = $0.60 \times 0.65 = 0.39$.
    • Expected profit = $0.39 \times 150,000 = 58,500$.
  • There is a 35% chance advertising does not stimulate demand, students remain at 40.
    • Profit for 40 students = GH¢115,000.
    • Net profit = $115,000 - 15,000 = 100,000$.
    • Probability = $0.60 \times 0.35 = 0.21$.
    • Expected profit = $0.21 \times 100,000 = 21,000$.

• Scenario B: Economic conditions are good (40% chance).

  • There is a 25% chance advertising stimulates demand, increasing students to 25.
    • Profit for 25 students = GH¢40,000.
    • Net profit = $40,000 - 15,000 = 25,000$.
    • Probability = $0.40 \times 0.25 = 0.10$.
    • Expected profit = $0.10 \times 25,000 = 2,500$.
  • There is a 75% chance advertising does not stimulate demand, students remain at 20.
    • Profit for 20 students = GH¢15,000.
    • Net profit = $15,000 - 15,000 = 0$.
    • Probability = $0.40 \times 0.75 = 0.30$.
    • Expected profit = $0.30 \times 0 = 0$.

The total expected profit if the programme is advertised is:

$$\text{Expected Profit (Advertising)} = 58,500 + 21,000 + 2,500 + 0 = \text{GH¢}82,000$$

• Expected Profit (No Advertising) = GH¢75,000
• Expected Profit (Advertising) = GH¢82,000

Since the expected profit from advertising (GH¢82,000) is higher than not advertising (GH¢75,000), the university should advertise the programme.

The final answer is $\boxed{\text{The university should advertise the programme, as it yields a higher expected profit of GH¢82,000.}}$