$[20]$ Ant Co$,$ has developed a new product, the A$-$Warren. It is now time to bring the A$-$Warren product to market. There are two choices for Ant$-$Co either market the product only in the local area, or market the product nationally $($Note: there is no choice of "not market" $-$ they have to choose one between "locally" and "nationally"$).$

If Ant Co$.$ rolls out the A$-$Warren product locally, it will cost $$100,000($ $$0\mathrm{.}1M)$ to advertise. If it is successful, then the company will receive $$1\mathrm{.}5M$ from product sales. However, if the local rollout is unsuccessful, then the company will receive nothing.

If Ant Co$.$ rolls out the A$-$Warren product nationally, it$,$ will cost $$1M$ to advertise. If it is successful, then the company will receive $$4M$ from product sales. However, if the national rollout is unsuccessful, then the company will receive nothing.

Historically, $30\%$ of Ant Co$.\text{'}$s product rollouts have been successful.

$($a$)[3]$ What is the best decision for Ant$-$Co with respect to the A$-$Warren and the associated expected monetary value $($EMV$)$ of the decision?

$($b$)[3]$ What is the most that Ant Co should pay for any information regarding the success of the A$-$Warren product $($Hint: This is the expected value of perfect information, or EVPI$)?$