Q$1.$ A manufactuxing firm which you control, is interested in investing in a new manufacturing technology, which has a promise to provide high quality outputs.

We assume that there is a probability of about $0\mathrm{.}6$ that the quality of products is indeed high and causes an increased profit of Rs $100$ crores $($on a net$-$present$-$value basis$).$ With probability $0\mathrm{.}4,$ there is hardly any increase in the quality, and hence there is no increase in the profits. The technology can be purchased at Rs $35$ crores.

Moreover, you also can decide right now to hire or not hire skilled staff to operate the new technology. If the technology actually produces high$-$quality products, then the skilled staff will increase the profit to Rs $110$ crores $($as opposed to Rs $100$ crores otherwise$).$ If the technology does not improve quality, then the skilled staff don't add much value. It costs you Rs $5$ crores to hire and pay the skilled staff $($on a net$-$present$-$value basis$).$

Draw decision tree you use to solve this problem

What is the smallest value of probability that the technology produces high$-$quality product, that you will purchase the technology?

Now suppose, you can hire your internal engineers to test the technology before you purchase it$.$ If your engineers say that the technology would work, there is a $70\%$ chance that the technology will actually work. If your engineers say that the technology will not work, there is a $90\%$ chance that it will not work.

How many rupees is this imperfect information by the engineer's worth?