During any period, a potential customer arrives at a certain facility with probability 1/2. If there aretwo people in the facility (including the one being served) the potential customer leaves the facilityimmediately and never returns. However, if there is one or fewer people, he enters the facility andbecomes an actual customer. The manager of the facility has two types of service rates available. Ifshe uses her slow service rate at a cost of $3 during a period, a customer will be served and leave thefacility with probability 3/5. If she uses her fast service rate at a cost of $9 during a period, a customerwill be served and leave the facility with probability 4/5. Note that the probability of more than onecustomer arriving or more than one customer being served in a period is 0. A profit of $50 is earnedwhen a customer is served. The manager wants to minimize the expected discounted cost of service over an infinite horizon β=0.9). Required:
a. Formulate the problem as a Markov decision process (e. g. specify the state space, decision set, transition probabilities, expected rewards) Hint: In computing the costs for services, do not forget the opportunity cost of losing a potential customer – e. g. 50$ is lost.
b. Formulate the problem as a linear program to determine the optimal stationary policy.
c. Implement the policy iteration algorithm starting with the stationary policy that always uses slow service. Iterate either until you find the optimal policy or implement 3 iterations.
d. Implement the value iteration algorithm for 3 iterations.
e. In the value iteration algorithm, what is the number of iterations necessary to achieve a desired precision of ε=0.1?

32/80  

91/140

the last one 54 doesn't go into 45. 54/100 ?

step-by-step explanation:

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)  

step-by-step explanation: the declaration of the rights of man and of the citizen (french: déclaration des droits de l'homme et du citoyen de 1789), set by france's national constituent assembly in 1789, is a human civil rights document from the french revolution.[1]

the declaration was drafted by the abbé sieyès and the marquis de lafayette, in consultation with thomas jefferson.[2] influenced by the doctrine of "natural right", the rights of man are held to be universal: valid at all times and in every place, pertaining to human nature itself. it became the basis for a nation of free individuals protected equally by the law. it is included in the beginning of the constitutions of both the fourth french republic (1946) and fifth republic (1958) and is still current. inspired by the enlightenment philosophers, the declaration was a core statement of the values of the french revolution and had a major impact on the development of freedom and democracy in europe and worldwide.[3]

the 1789 declaration, together with the 1215 magna carta, the 1689 english bill of rights (1689), the 1776 united states declaration of independence, and the 1789 united states bill of rights, inspired in large part the 1948 united nations universal declaration of human rights