A manager wants to create a portfolio of suppliers for the parts used in her company$$s products

that will represent a reasonable balance between costs and risks. While she knows that the singlesupplier approach has many potential benefits with respect to quality management and just$-$intime production, she also worries about the risk of fires, natural disasters, or other catastrophes at

supplier plants disrupting her firm$$s performance. Based on historical data and climate and

geological forecasts, the manager estimates the probability of a $$super$-$event$$ that would

negatively impact all suppliers simultaneously to be $5\%($i$.$e$.,$ probability $=0\mathrm{.}05)$ during the

supply cycle. She further estimates the $$unique event$$ risk for any of the potential suppliers to be

$10\%($i$.$e$.,$ probability $=0\mathrm{.}1).$ Assuming that the marginal cost of managing an additional supplier

is $$20,000,$ and the financial loss incurred if a disaster caused all suppliers to be down

simultaneously is $$500,000.$ Assume that up to three nearly identical suppliers are available.

a$)$ Calculate the probability of one supplier being disrupted, p$(1),$ when only one supplier

exists. $($Ans: $0\mathrm{.}145)$

b$)$ Calculate the probability of two suppliers being disrupted simultaneously, p$(2),$ when

there are two suppliers. $($ Ans: $0\mathrm{.}0595)$

c$)$ Calculate the probability of all three suppliers being disrupted simultaneously, p$(3),$ when

there are three suppliers. $($Ans: $0\mathrm{.}05095)$

d$)$ Draw the decision tree for the firm. Use the decision tree to calculate expected monetary

values $($EMVs$)$ for one supplier, for two suppliers, and for three suppliers. $($$$447,500\mathrm{.}00$;

$$510,250\mathrm{.}00$; $$534,525\mathrm{.}00)$