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 $\backslash (\backslash$$ $100,000\backslash )$ in research and development $($R$\backslash$&D$)$ activities. Even with the R$\backslash$&D$,$ there is only a $\backslash (40\backslash \%\backslash )$ chance of winning the contract. If Amber wins the contract, they will be able to sell $10,000$ motor assemblies at a price of $\backslash (\backslash$$ $100\backslash )$ 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 $\backslash (\backslash$$ $80,000\backslash )$ for modification of the current machines; in addition, variable $($per unit$)$ production cost will be $\backslash (\backslash$$ $40\backslash ).$ 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:

$-$ New technology: The cost of new technology is $\backslash (\backslash$$ $520,000\backslash ).$ Variable $($per unit$)$ cost per unit will be only $\backslash (\backslash$$ $20\backslash ),$ and there is no need for overtime since the new technology includes much faster machines.

Formulate the above problem as a decision tree. $($Suggestion: keep track of cash$/$payoff flows in units of $\backslash$$$1,000).$ SOLVE for the optimal strategy.