Math Problem Statement
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.
Assuming Mr. Annan has a third option of depositing the money at Ecobank which promises an assured Ghc 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
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Math Problem Analysis
Mathematical Concepts
Probability
Expected Value
Formulas
Expected Value formula: E(X) = Σ x * P(x)
Theorems
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Suitable Grade Level
High School
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