A company plans to buy a land of $10$ acres to build an industrial installation. The cost of the installa$-$

tion will be $25M.$ If the company decides to proceed with the investment, it will have the option to

expand the installation by buying an additional $5$ acres of land at a cost equal to the price of the land

initially bough. The construction cost for the expansion of the installation will be $10M.$ Considering

the outcomes for the initial investment and the expansion, the company has estimated the following

economic results:

Given that the success probabilities for the initial investment and the expansion are both equal to

$80\%,$ answer the following:

a$)$ Present the problem in the form of a decision tree.

b$)$ Use the decision tree to calculate the maximum amount that the company would be willing to

pay to buy the land.