art 1 of 1 Question 1 of 6 Mr. Annan is contemplating setting up a shopping mall in Acera or Sunyani but not both. Patronage could be high or low. He estimate there is a so\% chance patronage could be high in Accra with an associated profit of Ghe 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 advertiscment at an estimated cost of Ghe 70,000 per year or close down the business at a loss of Ghe - 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 ar close down at a cost of Ghe 50,000 . Advertisement in Accra has a $55 \%$ chance of generating high patronage at a profit of Ghe 140,000 per year or medium patronage at a profit of Gbe $65,0 \mathrm{OR} 0$ per year. Advertisement in Sunyani has a $65 \%$ chance of generating high patronage at a profit of Ghe 110,000 per year or medium patronage at a profit of Ghe 60,000 per year. Assuming Mr. Annan has a third option of depositing the money at Ecobank which promises an assured Ghe 40,000, which of the options will Mr Annan choose? Use 1,2 and 3 to represent Accra, Sunyani and the third option respectively.
Solution
Step 1 ：Calculate the expected profit for each option in Accra, Sunyani and Ecobank.
Step 2 ：For Accra, there are two scenarios: high patronage and low patronage. For high patronage, the profit is Ghe 140,000 and the probability is 50%. For low patronage, Mr. Annan can either advertise or close down. If he advertises, there is a 55% chance of high patronage with a profit of Ghe 140,000 and a 45% chance of medium patronage with a profit of Ghe 65,000. The cost of advertisement is Ghe 70,000. If he closes down, the loss is Ghe 150,000.
Step 3 ：For Sunyani, there are also two scenarios: high patronage and low patronage. For high patronage, the profit is Ghe 110,000 and the probability is 55%. For low patronage, Mr. Annan can either advertise or close down. If he advertises, there is a 65% chance of high patronage with a profit of Ghe 110,000 and a 35% chance of medium patronage with a profit of Ghe 60,000. The cost of advertisement is Ghe 15,000. If he closes down, the loss is Ghe 50,000.
Step 4 ：The third option is to deposit the money at Ecobank with a guaranteed profit of Ghe 40,000.
Step 5 ：Calculate the expected profit for each scenario in Accra and Sunyani, and compare it with the guaranteed profit in Ecobank.
Step 6 ：The expected profit in Accra is Ghe 88,125, in Sunyani is Ghe 95,375, and in Ecobank is Ghe 40,000.
Step 7 ：\(\boxed{\text{Final Answer: Mr. Annan should choose Sunyani. The expected profit in Sunyani is the highest among the three options. Therefore, the best choice for Mr. Annan is to set up the shopping mall in Sunyani.}}\)
