4. A fast-food chain has many hundreds of franchises nationwide. Ideally, each franchise would generate equal amounts of revenue for the chain, but in reality, some perform better than others. An internal audit reveals the following results: the lowest 30% of the franchises account for just 6% of the total revenue, the lowest 50% account for 20% of the total revenue, and the lowest 70% account for 43.5% of the total revenue. (Assume that 100% of the franchises account for 100% of the total revenue.) BURGER KING ?? Burger Chef DRIVE THRU ''M McDonald's Arby's BOAST BEEF Sandwich BURG

MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
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4. A fast-food chain has many hundreds of franchises
nationwide. Ideally, each franchise would generate
equal amounts of revenue for the chain, but in reality,
some perform better than others. An internal audit
reveals the following results: the lowest 30% of the
franchises account for just 6% of the total revenue,
the lowest 50% account for 20% of the total revenue,
and the lowest 70% account for 43.5% of the total
revenue. (Assume that 100% of the franchises
account for 100% of the total revenue.)
BURGER
KING
??
Burger
Chef
Drive Thru
BREAKFAST
DRIVE THRU
M
McDonald's
BILLION SEVED
DRIVE-THRU
Arby's
ROAST
BEEF
Sandwich
BURGER
KING
BURGER
KING
a) Use regression to determine a power function that
models these data, and write the Lorenz function
in the form f(x) = x". The coefficient should be
1, so you may have to do some rounding.
b) Determine the Gini coefficient and the Gini index.
c) What percentage of total revenue is generated by
the lowest 45% of the franchises?
d) What percentage of total revenue is generated by
the top 10% of the franchises?
Transcribed Image Text:4. A fast-food chain has many hundreds of franchises nationwide. Ideally, each franchise would generate equal amounts of revenue for the chain, but in reality, some perform better than others. An internal audit reveals the following results: the lowest 30% of the franchises account for just 6% of the total revenue, the lowest 50% account for 20% of the total revenue, and the lowest 70% account for 43.5% of the total revenue. (Assume that 100% of the franchises account for 100% of the total revenue.) BURGER KING ?? Burger Chef Drive Thru BREAKFAST DRIVE THRU M McDonald's BILLION SEVED DRIVE-THRU Arby's ROAST BEEF Sandwich BURGER KING BURGER KING a) Use regression to determine a power function that models these data, and write the Lorenz function in the form f(x) = x". The coefficient should be 1, so you may have to do some rounding. b) Determine the Gini coefficient and the Gini index. c) What percentage of total revenue is generated by the lowest 45% of the franchises? d) What percentage of total revenue is generated by the top 10% of the franchises?
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