A logistics provider plans to have a new warehouse built to handle increasing demands for its services. Although the company is unsure of how much demand there will be$,$ it must decide now on the size $($large or small$)$ of the warehouse. Preliminary estimates are that if a small warehouse is built and demand is low, the monthly income will be $$700,000.$ If demand is high, it will have to either expand the facility or lease additional space. Leasing will result in a monthly income of $$100,000$ while expanding will result in a monthly income of $$500,000.$

If a large warehouse is built and demand is low, monthly income will only be $$40,000,$ while if demand is high, monthly income will be $$2$ million.

Using a tree diagram, identify the choice that would be made using each of the four approaches for decision making under uncertainty.

a$.$ Maximin

Small warehouse

Large warehouse

b$.$ Maximax

Large warehouse

Small warehouse

c$.$ Laplace: Assume the probabilities of low and high demand to be $\mathrm{.}50$ each.

Small warehouse

Large warehouse

d$.$ Minimax regret