On May $1$st $2018$ PC Solutions Ltd won a contract worth $1\mathrm{.}2$m to develop a

customised piece of software for its largest customer Dilnot plc$.$ Dilnot requires the

software to be ready to use by September $19$th $2018$ and will only pay one third of

the contract value if the software is late. PC Solutions Ltd can either develop the

software in$-$house using its own staff, which will cost $600,000,$ or it can use a Tokyobased software company which will cost an additional $50\%$ on this cost.

If PC Solutions Ltd produces the software themselves there is a $10\%$ chance that

the project will not be completed by the deadline. The company in Tokyo is used to

responding quickly and would be guaranteed to produce the software on time. PC

Solutions Ltd will know whether the software is going to be delivered on time on July

$29$th $2018.$ If they know that the software will be late at that point, they can choose

to continue to produce the software locally, or to cancel the contract paying a

$100,000$ penalty to Dilnot plc$,$ or send it to the Tokyo$-$based company for completion

at a further cost $400,000$ with an $80\%$ chance that the software will still be

completed on time.Draw a decision tree for PC Solutions Ltd$.$ including all relevant data on the diagram.

Calculate the expected values for each decision point and recommend a

course of action for each decision point to PC Solutions Ltd$.$