<s>[INST] A proposed system uses a linear combination of the boxes: boxes A and B, boxes A and C, or boxes A, B and C, with the proportion of use of each box varying dependently on the state of the command vector. There are 150 different possible pairs of command vector states that can appear. The system would be used to make predictions with probabilities of correctness 7/10, 6/10 and 5/10. The utilities of correct and incorrect predictions, as well as the probabilities, are different for each command vector state. In one command vector state the utilities are u(correct) = $5500 and u(incorrect) = -$2000; in another they are u(correct) = $8000 and u(incorrect) = -$1000, and so on. Utilities associated with other command vector states have similar magnitudes. The system has 3 possible predictions, and the total number of possible states (command vector states, prediction outcomes) is 150  3  3 = 1350.[/INST]