Jose is a fruit vendor that purchases boxes of fruit from the neighboring farm. He classifies the boxes as satisfactory or unsatisfactory depending on the amount of excellent fruit they turn out to have. A satisfactory box contains 80 percent excellent fruit and will earn $200 profit for Jose. An unsatisfactory box contains 30 percent excellent fruit and will produce a loss of $1,000. About 90 percent of the boxes turn out to be of satisfactory quality, but the other 10 percent are unsatisfactory. Before Jose decides to accept a box, he is given the opportunity to sample one piece of fruit to test whether it is excellent. Based on that sample, he then has the option of rejecting the box without paying for it.

Develop a table for Jose's optimal policy according to the Bayes rule when he does the sampling and when he does not. Be sure to clearly show the profit that he makes in each scenario.