1.- You have the following manufacturing system: A B с 5% 15% M M1 M2 20% 20% E G 40% D H 40% M3 I 10% 60% F J 90% M4 K 15% L 85% Knowing that: * flow L denotes an OK (sellable) output; flows C, E, I, and K denote NOK (scraped) lots. * the selling price of OK (sellable) output = 10 ($/lot). * the cost of NOK (scraped) lot = 1 (S/lot). * the input rates - for A and B - are 5 lot/hr and 15 lot/hr (respectively). , calculate the total profit achieved in one hour ($/hr). 2.- For the previous manufacturing system, assume now that the service rate - for each Mi - is the following: M1 => µl = 4 lot/hr M2 => μ2 = 6 lot/hr M3 =>u3 = 8 lot/hr M4 => μ4= 5 lot/hr , calculate the value of incoming flows A and B so no Mi exceeds a Utilization (U) of 100%.

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Entropy

In physics, entropy means the amount of disorder or the degree of randomness associated with a thermodynamic system. The system is not self-organized when the entropy of the system is high. For instance, when a system is at an elevated temperature, its molecules are in random motion, vibrating and colliding with each other. During this scenario, the probability of finding a molecule at a particular place twice, is low. Under this circumstance, the system can be said to be in a high entropy.