Mike must work at least 18 hours a week to supplement his income while attending school. He has the opportunity to work in two retail stores. In store 1, he can work between 5 and 13 hours a week, and in store 2, he is allowed between 6 and 11 hours. Both stores pay the same hourly wage. In deciding how many hours to work in each store, Mike wants to base his decision on work stress. Based on interviews with present employees, Mike estimates that, on an ascending scale of 1 to 10, the stress factors are 8 and 6 at stores 1 and 2, respectively. Because stress mounts by the hour, he assumes that the total stress for each store at the end of the week is proportional to the number of hours he works in the store. How many hours should Mike work in each store?
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Mike must work at least 18 hours a week to supplement his income while attending school. He has the opportunity to work in two retail stores. In store 1, he can work between 5 and 13 hours a week, and in store 2, he is allowed between 6 and 11 hours. Both stores pay the same hourly wage. In deciding how many hours to work in each store, Mike wants to base his decision on work stress. Based on interviews with present employees, Mike estimates that, on an ascending scale of 1 to 10, the stress factors are 8 and 6 at stores 1 and 2, respectively. Because stress mounts by the hour, he assumes that the total stress for each store at the end of the week is proportional to the number of hours he works in the store. How many hours should Mike work in each store?
a) Define the decision variables
b) LP model
c) feasible region
d) optimal solution
e) final answer in statement form
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