Answer:
Kindly check explanation
Step-by-step explanation:
Given the data:
Medium-Scale Large-Scale
Expansion Profit Expansion Profit
x f(x) y f(y)
Low 50 0.2 0 0.2
Demand Medium 150 0.5 100 0.5
High 200 0.3 300 0.3
a. Compute the expected value for the profit associated with the two expansion alternatives.
Which decision is preferred for the objective of maximizing the expected profit?
Expected value for medium scale expansion profit :
Expected value (E) = Σ(X) * f(x)
Σ[(50 * 0.2) + (150 * 0.5) + (200 * 0.3)]
= 145
Expected value for Large scale expansion profit :
Expected value (E) = Σ(X) * f(x)
Σ[(0 * 0.2) + (100 * 0.5) + (300 * 0.3)]
= 140
Medium scale expansion profit is preferred as it has the highest expected value.
b. Compute the variance for the profit associated with the two expansion alternatives.
Which decision is preferred for the objective of minimizing the risk or uncertainty?
Variance (V) = Σ(X - E)² * f(x):
Variance for medium scale expansion profit :
V = [((50-145)^2 * 0.2) + ((150-145)^2 * 0.5) + ((200-145)^2 * 0.3) = 2725
Variance for Large scale expansion profit :
V = [((0-140)^2 * 0.2) + ((100-140)^2 * 0.5) + ((300-140)^2 * 0.3) = 12400
Smaller variance is required to minimize risk, Hence, choose the medium scale expansion profit.
