Certainly! This situation involves decision$-$making under uncertainty, and decision trees are a great way to visually represent the options and their potential outcomes. Let's start by constructing the decision tree and then proceed to calculate the Expected Monetary Value $($EMV$)$ for each model

Explanation:

Decision Tree:

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$/$ William $($$$10,000)--0\mathrm{.}4$

$/$ Demand

$/\backslash$ Harry $($$$8,000)----0\mathrm{.}2$

Decision

$\backslash /$ Charles $($$$6,000)--0\mathrm{.}4$

$\backslash$ Demand

$\backslash$ William $($$$15,000)-0\mathrm{.}4$

Step $2$

Calculation of EMV:

For each model and potential demand level, we'll calculate the EMV by multiplying the probability of each demand level by the respective profit and summing these values

Explanation:

William Model:

EMV $=(0\mathrm{.}4*$ $$10,000)+(0\mathrm{.}2*$ $$15,000)+(0\mathrm{.}4*$ $$14,000)=$ $$4,000+$ $$3,000+$ $$5,600=$ $$12,600$

Harry Model:

EMV $=(0\mathrm{.}4*$ $$8,000)+(0\mathrm{.}2*$ $$18,000)+(0\mathrm{.}4*$ $$12,000)=$ $$3,200+$ $$3,600+$ $$4,800=$ $$11,600$

Charles Model:

EMV $=(0\mathrm{.}4*$ $$6,000)+(0\mathrm{.}2*$ $$16,000)+(0\mathrm{.}4*$ $$21,000)=$ $$2,400+$ $$3,200+$ $$8,400=$ $$14,000$

Answer

Conclusion:

Based on the EMV calculations:

William Model has an EMV of $$12,600$

Harry Model has an EMV of $$11,600$

Charles Model has an EMV of $$14,000$

Therefore, the Charles Model has the highest Expected Monetary Value, making it the best choice among these three models considering the given range of demand. It's the most profitable option, considering the probabilities associated with different demand levels.