A gardner can use one of three brandsof fertilizers during the next growing seas

Question

A gardner can use one of three brandsof fertilizers during the next growing season. The following decision table shows the expeted gross income per acre for each fertilizer brand and weather condition for the growing season.

The chance of a dry season is shown by probability P. Find the P range values where iusing Brand B fertilizer has the highest expected returns compared to the alternative fertilizer brands.

                                                              Season

                                                      Dry           Wet

Fertilizers      BRAND A                110             60

                      BRAND B                 100             140

                     BRAND C                 80             160

Explanation / Answer

returns = R = probability of dry season x returns + probability of wet season x return; R = 100p + 140(1-p) > 110p + 60(1-p), 80p + 160(1-p);

R = 140 - 40p > 50 + 60p; 140 - 40p > 160 - 80p;

90 > 100p; 40p > 20;

p<0.9; p>0.5;

0.5 < p < 0.9

so p = (0.5, 0.9) Ans

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