Question

Compute the variation for the profit associated with the two expansion alternatives. Which decision is preferred for the objective of minimizing the risk of uncertainty? Complete the table and provide explanation of results.

Medium-Scale Expansion Profits Annual Profit ($1000s) P(x) 50 20% 1501 50% 200 30% Large-Scale Expansion Profits Annual Profit ($1000s) P(x) 01 20% 100 50% 300 30% Low Demand Medium High 1 Expected Profit ($1000) (x) Risk Analysis for Medium-Scale Expansion Annual Profit Probability Demand $1000s P(x) (x-4) (x-H)² [(x - 1)? * P(x)| Low 50 20% Medium 150 50% High 200 30%|| Risk Analysis for Large-Scale Expansion Annual Profit (x) Probability Demand $1000s P(x) (x - 1) (x - 1) 0 20% Medium 100 50% High 300 30% (x - ** P(x) Low

Answer 1

Solution:

Medium-Seale ХР(x) ХР(х) Large-Seale Expansion Profits P(x) P(x) X Expansion Profits Annual 20% 20% 50 10 0 0 Annual 50% 50% 150 75 100 50 Profit Profit 30% 30% 200 60 300 90 ($1000s) 50 ($1000s) Р(x) 20% 50% 30% P(x) 20% 50% Low Demand Medium ExP(x)140 xP(x) 145 0 150 100 High 200 300 30% Expected -value =2xP(x)=145 Expected -value = xP(x) = 140 Expected Profit ($1000s) 145 140

Risk Analysis for Medium-Scale Expansion Annual Profit (x) (х- м)" (x-u)P(x) (х-и) ХP(x) Р(x) X 20% 50 10 -95 9025 1805 Probability P(x) 50% 150 75 5 25 13 Demand $1000s |(x -u) ( x-u) P(x) |(x-H) 20% 30% 200 60 55 3025 908 Low Medium High 50 -95 9025 1805 o x-u)*P(x) = 2725 LL= 145 50% 5 30% 55 150 25 13 200 3025 908 (х- и)** Р(х) %3D 52.20 2725 52.20 (x-u) (x-u)2P(x) ХP(x) (х-м) P(x) х Risk Analysis for Large-Scale Expansion Annual Profit |(х) 20% 0 -140 19600 3920 50% 1600 100 50 -40 800 Probability |Р'x) 0 30% 300 90 25600 7680 |(x-u |(x-u) P(x) (х - ) Demand $1000s a2 x)*P(x) =12400 L 140 20% -140 19600 3920 Low E (х-и)?* Р(х) %3D111.3553 | Medium High 50% 100 -10 1600 800 30% 160 300 25600 7680 12400 111.3553

The expected profit for medium scale expansion is $145 (in 1000s) with a standard deviation of 52.20( in 1000s)

The expected profit for large scale expansion is $140 (in 1000s) with a standard deviation of 111.3553( in 1000s)

Since the standard deviation for medium scale expansion is lesser, therefore, for the objective of minimizing the risk of uncertainty, the decision of medium scale expansion is preferred