Question

You sell tomatoes in a market. You do not know in advance the number of cases of tomatoes that will be sold tomorrow, but you must decide today how many cases to stock in order to maximize profits. You can purchase tomatoes for =N=3,000 per case and sell them for =N=8,000 per case. The tomatoes have no value after the first day that they are offered for sale. An analysis of past sales has given you the following information: Cases Sold Daily Probability 0.2 0.4 0.3 0.1 10 11 12 13 A. Construct the pay-off matrix. (6 marks) B. What decision is recommended by Maximum Likelihood approach? (4 marks)​

Answer 1

a) The pay-off matrix can be obtained by multiplying the number of cases sold daily by their probabilities.

b) The recommended decision is to stock the number of cases with the highest probability.

Step-by-step explanation:

a) To construct the pay-off matrix, we need to multiply the number of cases sold daily by the probability of that number of cases being sold.

The pay-off matrix would look as follows:

Cases_Sold Daily_Probability

10 0.2

11 0.4

12 0.3

13 0.1

b) The decision recommended by the Maximum Likelihood approach is to stock the number of cases that has the highest probability, which in this case is 11 cases (0.4 probability).