How to solve $($Subject: operations management$)$

A firm that plans to expand its product line must decide whether to build a small or a large facility to produce the new products.

If it builds a small facility and demand is low, the profit will be $$405,000.$ If demand is high, the firm can either maintain the small facility or expand it$.$ The expansion would have a profit of $$520,000,$ and maintaining the small facility would have a profit of $$50,000.$

If a large facility is built and demand is high, the profit will be $$780,000.$ If demand turns out to be low, the profit will be $-$$$10,000.$

The probability that demand will be high is estimated to be $0\mathrm{.}70,$ and the probability of low demand is estimated to be $0\mathrm{.}3.$

a$.$ Construct a decision tree to select the proper size of plant $(3$ pts $).$

b$.$ What is the expected payoff of building small facility? $(1\mathrm{.}5$ pts$)$

c$.$ What is the expected payoff of building large facility? $(1\mathrm{.}5$ pts$)$

d$.$ Which option $($building small vs$.$ large facility$)$ should be selected? Why? $(1$ pts$)$