22. Lawson's Department Store faces a buying decision for a seasonal product for which demand can be high, medium, or low. The purchaser for Lawson's can order one, two, or three lots of the product before the season begins but cannot reorder later. Profit project tions (in thousands of dollars) are shown. State of Nature High Demand Medium Demand Low Demand Decision Alternative $1 $2 $3 Order 1 lot, d, 60 60 50 Order 2 lots, d, 80 80 30 Order 3 lots, d3 100 70 10 a. If the prior probabilities for the three states of nature are 0.3, 0.3, and 0.4, respectively, what is the recommended order quantity? b. At each preseason sales meeting, the vice president of sales provides a personal opinion regarding potential demand for this product. Because of the vice president's enthusiasm and optimistic nature, the predictions of market conditions have always been either "excellent" (E) or "very good" (V). Probabilities are as follows: P(E) = 0.70 P(s | E) = 0.34 P(s] [ V) = 0.20 P(V) = 0.30 P(s, | E) = 0.32 P(s, | V) = 0.26 P(s, | E) = 0.34 P(s, | V) = 0.54 What is the optimal decision strategy? c. Use the efficiency of sample information and discuss whether the firm should consider a consulting expert who could provide independent forecasts of market conditions for the product