Key information

$$ A national launch would mean distributing $60,000$ coffee containers

$$ A local test would mean $($initially$)$ distributing just $5,000$ containers within a single city $($and then having the option of considering a subsequent national launch on the remaining $60,0005,000=55,00$ containers$)$

More specifically, if no testing has been done then success would be selling all $60,000$ containers.

If local testing succeeds $($i$.$e$.,$ if all $5,000$ containers sold$)$ then success would be selling the remaining $60,0005,000=55,000.$

If local testing fails $($i$.$e$.,$ if none of the $5,000$ containers sell$)$ then success would again be selling the remaining $60,0005,000=55,000.($ too expensive to retrieve the local batch$)$

Decision Chance of success $($selling all $[$remaining$]$ containers$)$

No local testing $55\%$

Local testing succeeds $85\%$

Local testing fails $25\%$

Local testing, if done, has a $50\%$ chance of selling all $5,000$ containers and a $50\%$ chance of selling $0$ containers.

Packaging and shipping: $$45,000$ cost fixed, but paid each time that a test or launch occurs. $($This will be $0$ or $1$ or $2$ times, depending upon the adopted strategy.$)$

Packaging and shipping: $$10$ cost per container

Branding $$50,000$ cost fixed, only has to be paid once $($This will be $0$ or $1$ times, depending upon the adopted strategy.$)$

Sale price $$20$ revenue per container

For each local test and$/$or national launch, packaging and shipping is paid each time. If there is a test and$/$or a national launch, then the cost of branding occurs exactly once.

Determine whether the FairBean should launch nationally or locally test first. And, if testing locally first, give further details as appropriate. Provide decisions to be made, including expected financial returns.

a$.$ find the valuation for this problem and to show the decisions you would make at each node where a decision is made.

b$.$ what would be the expected value of perfect information $($EVPI$)?$

c$.$ Make a final recommendation on national or local launch, or neither. Justify