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 2nd machine is taken later after seeing high demand. Jane estimates that demand may be low with a probability of 0.25, or medium with a probability of 0.3, or high with a probability of 0.45 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 2nd 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 490,000$ and doing nothing gives a payoff of 250,000$ Solve the decision tree. What is the expected pay-off? Enter your answer rounded to the nearest dolla

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter9: Decision Making Under Uncertainty

Section: Chapter Questions

Problem 30P

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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 2nd machine is taken later after seeing high demand.

Jane estimates that demand may be low with a probability of 0.25, or medium with a probability of 0.3, or high with a probability of 0.45
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 2nd 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 490,000$ and doing nothing gives a payoff of 250,000$

Solve the decision tree. What is the expected pay-off? Enter your answer rounded to the nearest dollar.

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