Recall the model
for Paul’s and Bob’s cafes, where x(t) is Paul’s daily profit, y(t) is Bob’s daily profit, and a, b, c, and d are parameters governing how the daily profit of each store affects the other. In Exercise, different choices of the parameters a, b, c, and d are specified. For each exercise write a brief paragraph describing the interaction between the stores, given the specified parameter values. [For example, suppose a = 1, c = -1, and b = d = 0. If Paul’s store is making a profit (x > 0), then Paul’s profit increases more quickly (because ax > 0). However, if Paul makes a profit, then Bob’s profits suffer (because cx<0). Since b = d = 0, Bob’s current profits have no impact on his or Paul’s future profits.]
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