Hello can you please help me with a step by step guide for letters G and H. Thank you very much! You work for a large conglomerate of 100 associated companies. In order to avoid antitrust issues with the DOJ, you need to divide the 100 companies into 4 different groups such that: 1. Companies within the same group cannot do business with each other. 2. Companies in different groups can do business with each other. What organization of the 100 companies into the 4 groups maximimizes the number of business opportunities? a) Start by labeling the groups X , Y , Z , and W . Let x = the number of companies assigned to group X and so on for the other groups. Construct an equation in x for the number of business opportunities for a company in group X — i.e., how many companies can that company do business with? b) Nowbuildanequationinxforthetotalnumberofbusinessopportunitiesforallcompanies in group X. c) Do likewise for the remaining groups and construct a function f (x, y, z, w) that gives the total number of business opportunities across all the groups. d) What is the constraint on x, y, z, and w? e) Introduce a Lagrange multiplier λ and determine fx = λgx, where g is the function con- structed from the above constraint. f) Do likewise for fy, fz, and fw, and combine them with the constraint so that you have 5 equations in 5 unknowns. g) Use substitution to determine a value for λ. h) Substitute the value for λ into the other equations to determine the optimal distribution of companies into the 4 groups.
Hello can you please help me with a step by step guide for letters G and H. Thank you very much!
You work for a large conglomerate of 100 associated companies. In order to avoid antitrust issues with the DOJ, you need to divide the 100 companies into 4 different groups such that:
1. Companies within the same group cannot do business with each other.
2. Companies in different groups can do business with each other.
What organization of the 100 companies into the 4 groups maximimizes the number of business opportunities?
a) Start by labeling the groups X , Y , Z , and W . Let x = the number of companies assigned to group X and so on for the other groups. Construct an equation in x for the number of business opportunities for a company in group X — i.e., how many companies can that company do business with?
b) Nowbuildanequationinxforthetotalnumberofbusinessopportunitiesforallcompanies in group X.
c) Do likewise for the remaining groups and construct a function f (x, y, z, w) that gives the total number of business opportunities across all the groups.
d) What is the constraint on x, y, z, and w?
e) Introduce a Lagrange multiplier λ and determine fx = λgx, where g is the function con-
structed from the above constraint.
f) Do likewise for fy, fz, and fw, and combine them with the constraint so that you have 5 equations in 5 unknowns.
g) Use substitution to determine a value for λ.
h) Substitute the value for λ into the other equations to determine the optimal distribution of companies into the 4 groups.
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