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Demand has grown at Dairy May Farms, and it is considering expanding. One option is to expand by purchasing a very large farm that will be able to meet expected future demand. Another option is to expand the current facility by a small amount now and take a waitand$-$see attitude, with the possibility of a larger expansion in two years.

Management has estimated the following chances for demand:

The likelihood of demand being high is $0\mathrm{.}68.$

The likelihood of demand being low is $0\mathrm{.}32.$

Profits for each alternative have been estimated as follows:

Large expansion has an estimated profitability of either $$48,900$ or $$23,000,$ depending on whether demand turns out to be high or low.

Small expansion has a profitability of $$14,200,$ assuming that demand is low.

Small expansion with an occurrence of high demand would require considering whether to expand further. If the company expands at that point, the profitability is expected to be $$39,100.$ If it does not expand further, the profitability is expected to be $$11,910.$

$($b$)$ Calculate expected values for large and small expansions. What should Dairy May Farms do$?$

$E{V}_{\text{s}\text{m}\text{a}\text{l}\text{l}\text{e}\text{x}\text{p}\text{a}\text{n}\text{s}\text{i}\text{o}\text{n}}=$$

$E{V}_{\text{l}\text{a}\text{r}\text{g}\text{e}\text{e}\text{x}\text{p}\text{a}\text{n}\text{s}\text{i}\text{o}\text{n}}=$$

Company sould opt

expansion.

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