Mr. Annan is contemplating setting up a shopping mall in Accra or Sunyani but not both. Patronage could be high or low. He estimate there is a 50% chance patronage could be high in Accra with an associated profit of Ghc 140,000 per year, and 55% chance patronage could be high in Sunyani with a profit of 110,000 per year. If in Accra and patronage is low, he can either put in an aggressive advertisement at an estimated cost of Ghc 70,000 per year or close down the business at a loss of Ghc -150,000. Similarly, if in Sunyani and patronage is low, he can put in an aggressive advertisement at an estimated cost of 15,000 per year or close down at a cost of Ghc 50,000. 

Advertisement in Accra has a 55% chance of generating high patronage at a profit of Ghc 140,000 per year or medium patronage at a profit of Ghc 65,000 per year. Advertisement in Sunyani has a 65% chance of generating high patronage at a profit of Ghc 110,000 per year or medium patronage at a profit of Ghc 60,000 per year.  

What is the net gain in choosing Sunyani over Accra for the shopping mall? **Your answer must be in two (2) decimal places Ghc**   

To determine the net gain in choosing Sunyani over Accra for the shopping mall, we need to calculate the expected profit for both locations. Here is the step-by-step process:

### Expected Profit in Accra

1. **High Patronage:**
   - Probability: 50%
   - Profit: Ghc 140,000 per year

2. **Low Patronage:**
   - Probability: 50%
   - Actions: Advertise or close down

   - **Advertisement:**
     - Cost: Ghc 70,000 per year
     - High Patronage:
       - Probability: 55%
       - Profit: Ghc 140,000 per year
     - Medium Patronage:
       - Probability: 45%
       - Profit: Ghc 65,000 per year

     \[
     \text{Expected profit after advertisement} = 0.55 \times 140,000 + 0.45 \times 65,000 - 70,000
     \]

     \[
     = 77,000 + 29,250 - 70,000 = 36,250 \text{ Ghc}
     \]

   - **Close down:**
     - Loss: Ghc 150,000 per year

   Comparing the two options, advertisement yields a lower loss compared to closing down. So we choose to advertise.

   \[
   \text{Expected profit for low patronage} = 36,250 \text{ Ghc}
   \]

3. **Total Expected Profit in Accra:**

\[
\text{Expected profit in Accra} = 0.50 \times 140,000 + 0.50 \times 36,250
\]

\[
= 70,000 + 18,125 = 88,125 \text{ Ghc}
\]

### Expected Profit in Sunyani

1. **High Patronage:**
   - Probability: 55%
   - Profit: Ghc 110,000 per year

2. **Low Patronage:**
   - Probability: 45%
   - Actions: Advertise or close down

   - **Advertisement:**
     - Cost: Ghc 15,000 per year
     - High Patronage:
       - Probability: 65%
       - Profit: Ghc 110,000 per year
     - Medium Patronage:
       - Probability: 35%
       - Profit: Ghc 60,000 per year

     \[
     \text{Expected profit after advertisement} = 0.65 \times 110,000 + 0.35 \times 60,000 - 15,000
     \]

     \[
     = 71,500 + 21,000 - 15,000 = 77,500 \text{ Ghc}
     \]

   - **Close down:**
     - Loss: Ghc 50,000 per year

   Comparing the two options, advertisement yields a profit compared to closing down. So we choose to advertise.

   \[
   \text{Expected profit for low patronage} = 77,500 \text{ Ghc}
   \]

3. **Total Expected Profit in Sunyani:**

\[
\text{Expected profit in Sunyani} = 0.55 \times 110,000 + 0.45 \times 77,500
\]

\[
= 60,500 + 34,875 = 95,375 \text{ Ghc}
\]

### Net Gain in Choosing Sunyani over Accra

\[
\text{Net gain} = \text{Expected profit in Sunyani} - \text{Expected profit in Accra}
\]

\[
= 95,375 - 88,125 = 7,250 \text{ Ghc}
\]

Thus, the net gain in choosing Sunyani over Accra for the shopping mall is \( \boxed{7,250.00} \text{ Ghc} \).

Do you want details or have any questions?

Here are 8 related questions to expand on the information:
1. How do probability calculations affect business decision-making?
2. What is the impact of advertising costs on expected profits?
3. How can businesses use expected value in their planning?
4. What are the potential risks of choosing a location with high variability in patronage?
5. How would different advertisement effectiveness rates alter the expected profits?
6. What strategies can businesses use if the advertisement doesn't yield the expected results?
7. How would changes in the probability of high patronage impact the decision?
8. What other factors should Mr. Annan consider when choosing the location for the mall?

**Tip:** When evaluating business decisions, it's crucial to consider both expected profits and potential risks, including variability in outcomes and costs.

Explore how to calculate the net gain in choosing Sunyani over Accra for a shopping mall, based on probabilities and expected profits. Understand the impact of patronage variability and advertising costs on business decisions.

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