Which of the following is TRUE about the northwest-corner rule? A. All allocations are based on lowest cost B. All demand and s
upply constraints are satisfied, but cost is ignored C. All demand and supply constraints are satisfied while minimizing cost D. All demand and supply constraints are ignored while minimizing cost
1 answer:
Answer:
B. All demand and supply constraints are satisfied, but cost is ignored
Step-by-step explanation:
The northwest-corner rule is a method to compute the initial feasible solution of a transportation problem.
In this method you start to supply the demand with the northwest-corner option without taking into account the related cost. You assign the whole production of the first source to first demand, if that is more than necessary, then you assign the excess to the second demand, and so on; but if is not enough, then you assign the whole production of the next source to unsatisfied demand. Repeat this procedure until all demands are satisfied.
In the picture attached, an example is given. The table shows the unit transportation cost and in the circles the feasible solution obtained with northwest-corner rule.
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You can see the three diagram attached. Each link is labeled with the probability: you have probability 1/6 that a six is rolled, and 5/6 that it is not rolled.
To answer the questions, find the path that brings you to the desired outcome, and multiply all the labels you meet.
First question:
To get three sixes, you have to choose the left path at each roll. The probability is always 1/6, so the answer is
Second question:
To get no sixes, you have to choose the right path at each roll. The probability is always 5/6, so the answer is
Third question:
To get exactly one six, it can either be the first, second or third roll.
In all cases, you have to choose the left path once and the right path twice: left-right-right mean that you get the six in the first roll, right-left-right means that you get the six in the second roll, right-right-left means that you get the six in the third roll.
In every case, the left turn has probability 1/6, and the right turn has probability 5/6. The probability of each combination is thus
And since there are three of these combinations, The answer is
Fourth question:
Since the question suggests to use what we already achieved, let's do it: having at least one six is the complementary event of having no sixes at all. If an event has probability p, its complementary has probability 1-p. So, since the probability of no sixes is known, the probability of at least one six is
