3. Consider the following decision problem: Vegetable Farms is a small, family-operated ranch that sells produce to local markets. The owners are currently trying to decide whether they should expand their operation next year. Because this is a fairly new business, the owners have assessed the following demand levels and probabilities: high (probability 0.50), medium (0.30), or low (0.20). The payoffs they expect for each demand/acreage scenario are listed. Use a decision tree to help decide whether to expand the farm. (1) Develop an influence diagram for the owners to model the problem they face. Consider all uncertainties that you see necessary (demand should be one, of course.) Make appropriate assumptions if necessary. (2) Develop a decision tree for the owners of Vegetable Farms (3) Evaluate the tree and recommend which altemative the owners should take. 4. Consider the following problem: Aquatech currently holds the lease to at site with good potential for geothermal development to generate electricity. Aquatech is now looking at three options for the site: (1) sell the rights to the property for $1.5 million; (2) extend the lease for 25 years at a cost of $0.5 million, with the possibility of selling later; or (3) extend the lease and drill exploratory wells at a total cost of $2 million. If the company decides to extend the lease in order to drill, future revenue from the site would be determined by the temperature of the water. The following chart lists the probabilities associated with the three states of nature possible, along with the projected drill revenues: If the company extends the lease in order to sell the property later without drilling the sale price will be determined by the demand for electricity. The following chart lists the probabilities associated with the three levels of demand and the projected sale prices Use a decision tree to analyze this problem and determine which option the management should choose