Problem $4$ Decision Tree $(25$ points$)$

The Amber Corp. is faced with the decision as to whether or not to make a bid for producing a new motor assembly for a large automobile producer. If Amber decides to bid, this will cost them $$100,000$ in research and development $($R&D$)$ activities. Even with the R&D$,$ there is only a $40\%$ chance of winning the contract. If Amber wins the contract, they will be able to sell $10,000$ motor assemblies at a price of $$100$ per assembly. To produce these $10,000$ motor assemblies, they can choose to use existing technology or new technology as detailed below:

Existing technology: This will cost $$80,000$ for modification of the current machines; in addition, variable $($per unit$)$ production cost will be $$40.$ In addition, the current machines are not as fast as desired, and there is a chance that overtime $($OT$)$ costs will be incurred $($depending on other business activity at Amber$)$ as described in the following table:

$\backslash$table$[[\backslash$table$[[$Other business$],[$activity$]],$Probability,$\backslash$table$[[$Overtime$],[$cost$]]],[$Heavy$,\mathrm{.}2,$$$400,000$