Tree Diagram Bills

This is from Sanjoy Mahajan’s The Art of Insight Problem 1.5

Make a tree diagram for your estimate in Problem 1.3. Do it in three steps: (1) Draw the tree without any leaf estimates, (2) estimate the leaf values, and (3) propagate the leaf values upward to the root.

This is referring to the suitcase of money.

Step 1: Tree

graph LR;
   VolBankNote[Volume of Bank Note]
   VolSuitcase[Volume of Suitcase]
   ValueBankNote[Value of Bank Notes in Suitcase]
   NumBankNote[Number of Bank Notes in Suitcase]
   ValueSuitcase[Value of Suitcase]
   
   
   NumBankNote --> ValueSuitcase
   ValueBankNote --> ValueSuitcase

   VolBankNote -->|-1| NumBankNote
   VolSuitcase --> NumBankNote

   SuitWidth[Width of Suitcase] --> VolSuitcase
   SuitHeight[Height of Suitcase] --> VolSuitcase
   SuitDepth[Depth of Suitcase] --> VolSuitcase
   
   BankHeight[Height of Bank Note] --> VolBankNote
   BankWidth[Width of Bank Note] --> VolBankNote
   BankDepth[Thickness of Bank Note] --> VolBankNote

Step 2: Annotated Leaves

graph LR;
   VolBankNote[Volume of Bank Note]
   VolSuitcase[Volume of Suitcase]
   ValueBankNote[Value of Bank Notes in Suitcase<br>$100]
   NumBankNote[Number of Bank Notes in Suitcase]
   ValueSuitcase[Value of Suitcase]
   
   
   NumBankNote --> ValueSuitcase
   ValueBankNote --> ValueSuitcase

   VolBankNote -->|-1| NumBankNote
   VolSuitcase --> NumBankNote

   SuitWidth[Width of Suitcase<br/>30cm] --> VolSuitcase
   SuitHeight[Height of Suitcase<br/>50cm] --> VolSuitcase
   SuitDepth[Depth of Suitcase<br/>30cm] --> VolSuitcase
   
   BankHeight[Height of Bank Note<br/>15cm] --> VolBankNote
   BankWidth[Width of Bank Note<br/>6cm] --> VolBankNote
   BankDepth[Thickness of Bank Note<br/>0.01cm] --> VolBankNote

Step 3: Propagate

graph LR;
   VolBankNote[Volume of Bank Note<br>1 cm<sup>3</sup>]
   VolSuitcase[Volume of Suitcase<br>50L]
   ValueBankNote[Value of Bank Notes in Suitcase<br>$100]
   NumBankNote[Number of Bank Notes in Suitcase<br>50,000]
   ValueSuitcase[Value of Suitcase<br>$5 Million]
   
   
   NumBankNote --> ValueSuitcase
   ValueBankNote --> ValueSuitcase

   VolBankNote -->|-1| NumBankNote
   VolSuitcase --> NumBankNote

   SuitWidth[Width of Suitcase<br/>30cm] --> VolSuitcase
   SuitHeight[Height of Suitcase<br/>50cm] --> VolSuitcase
   SuitDepth[Depth of Suitcase<br/>30cm] --> VolSuitcase
   
   BankHeight[Height of Bank Note<br/>15cm] --> VolBankNote
   BankWidth[Width of Bank Note<br/>6cm] --> VolBankNote
   BankDepth[Thickness of Bank Note<br/>0.01cm] --> VolBankNote