Jane Woodhurst is considering whether to buy one or two machines for a certain stage of the assembly line at a new electric car startup company. If one machine is purchased initially, a second one can be purchased later after observing demand. However buying the machines together is cheaper. Also the lead time to get a machine is long, so there may be lost sales if the decision to buy the $2$nd machine is taken later after seeing high demand.

Jane estimates that demand may be low with a probability of $0\mathrm{.}25,$ or medium with a probability of $0\mathrm{.}3,$ or high with a probability of $0\mathrm{.}45.$

If two machines are purchased the payoffs are $90,000$$ for low demand, $200,000$$ for medium demand, and $500,000$$ for high demand.

If one machine is purchased, then no additional decision is required if the demand is low or medium $($as one machine can handle these cases$).$ However if the demand is high, Jane has $3$ options: outsource some production, buy a $2$nd machine, do nothing $($live with $1$ machine$).$

If one machine is purchased, and demand is low the payoff is $120,000$$ and if demand is medium the payoff is $250,000$$$.$

If one machine is purchased and demand is high, then outsourcing gives a payoff of $300,000$$$,$ purchasing a second machine gives a payoff of $400,000$$ and doing nothing gives a payoff of $250,000$$$.$

Make and solve a decision tree to hep Jane make the decision.

What is the expected pay$-$off for Jane? Enter your answer rounded to the nearest dollar.