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Bellman explains the reasoning behind the term dynamic programming in his autobiography, Eye of the Hurricane: An Autobiography (1984). He explains:\r\n\r\n\"I spent the Fall quarter (of 1950) at RAND. My first task was to find a name for multistage decision processes. \r\nAn interesting question is, Where did the name, dynamic programming, come from? \r\nThe 1950s were not good years for mathematical research. We had a very interesting gentleman in Washington named Wilson. He was Secretary of Defense, and he actually had a pathological fear and hatred of the word research.\r\n I\'m not using the term lightly; I\'m using it precisely. His face would suffuse, he would turn red, and he would get violent if people used the term research in his presence. You can imagine how he felt, then, about the term mathematical. \r\nThe RAND Corporation was employed by the Air Force, and the Air Force had Wilson as its boss, essentially. Hence, I felt I had to do something to shield Wilson and the Air Force from the fact that I was really doing mathematics inside the RAND Corporation. What title, what name, could I choose? In the first place I was interested in planning, in decision making, in thinking. But planning, is not a good word for various reasons. I decided therefore to use the word \"programming\".\r\n I wanted to get across the idea that this was dynamic, this was multistage, this was time-varying I thought, lets kill two birds with one stone. Lets take a word that has an absolutely precise meaning, namely dynamic, in the classical physical sense. It also has a very interesting property as an adjective, and that is it\'s impossible to use the word dynamic in a pejorative sense. Try thinking of some combination that will possibly give it a pejorative meaning. It\'s impossible.\r\n Thus, I thought dynamic programming was a good name. It was something not even a Congressman could object to. So I used it as an umbrella for my activities.\"\r\nThe word dynamic was chosen by Bellman to capture the time-varying aspect of the problems, and because it sounded impressive.[3] The word programming referred to the use of the method to find an optimal program, in the sense of a military schedule for training or logistics. This usage is the same as that in the phrases linear programming and mathematical programming, a synonym for mathematical optimization.[4]Optimal consumption and saving[edit]\r\nA mathematical optimization problem that is often used in teaching dynamic programming to economists (because it can be solved by hand[9]) concerns a consumer who lives over the periods t=0,1,2,\\ldots,T and must decide how much to consume and how much to save in each period.\r\n\r\nLet c_t be consumption in period t, and assume consumption yields utility u(c_t)=\\ln(c_t) as long as the consumer lives. Assume the consumer is impatient, so that he discounts future utility by a factor b each period, where 0<b<1. Let k_t be capital in period t. Assume initial capital is a given amount k_0>0, and suppose that this period\'s capital and consumption determine next period\'s capital as k_{t+1}=Ak^a_t - c_t, where A is a positive constant and 0<a<1. Assume capital cannot be negative. Then the consumer\'s decision problem can be written as follows:\r\n\r\n\\max \\sum_{t=0}^T b^t \\ln(c_t) subject to k_{t+1}=Ak^a_t - c_t \\geq 0 for all t=0,1,2,\\ldots,T\r\nWritten this way, the problem looks complicated, because it involves solving for all the choice variables c_0, c_1, c_2, \\ldots , c_T. (Note that k_0 is not a choice variable--the consumer\'s initial capital is taken as given.)