Develop a decision tree to evaluate the expected monetary value $($EMV$)$ of three potential expansion strategies for a retail company under different market conditions. Use the following decision alternatives and market conditions:

Decision Alternatives:

$1.$ Open a New Store

$2.$ Launch an Online Sales Platform

$3.$ Expand Product Lines in Existing Stores

Market Conditions:

$$ Strong Growth $($probability: $0\mathrm{.}4)$

$$ Moderate Growth $($probability: $0\mathrm{.}4)$

$$ Decline $($probability: $0\mathrm{.}2)$

Expected Monetary Values $($EMVs$)$ for Each Strategy:

$1.$ Open a New Store:

o Strong Growth: $$500,000$

o Moderate Growth: $$200,000$

o Decline: $-$$$100,000$

$2.$ Launch an Online Sales Platform:

o Strong Growth: $$300,000$

o Moderate Growth: $$150,000$

o Decline: $$0$

$3.$ Expand Product Lines in Existing Stores:

o Strong Growth: $$250,000$

o Moderate Growth: $$100,000$

o Decline: $-$$$50,000$

Calculate the EMV for each strategy under these market conditions and determine the optimal strategy for the company. Submit a report explaining your analysis and conclusion.