Bill, Susan and Joe bought a pizza which was 1/3 pepperoni (P), 1/3
sausage (S), and 1/3 mushrooms (M). See the diagram where the three sections
are labeled P, S, and M for the three toppings. In the diagram the
three sections don't look like they are the same size, but they
are supposed to
be...just use your imagination (It's not easy to draw with a mouse!).
They paid $12.00 for the pizza, with each person contributing $4.00.
Bill hates mushrooms, but he likes pepperoni and sausage equally well.
1. What is the value to Bill of the M third?
2. What is the value to Bill of the P third?
3. What is the value to Bill of the S third?
They decided to split the pizza using the lone divider method, with
Susan the divider. She cut the pizza as shown in the diagram, with
a green piece, a yellow piece and a blue piece. Note that green
includes 1/2 of the pepperoni
and 1/4 of the mushrooms; blue contains 1/2 of the pepperoni and
1/4
of the sausage; yellow contains 3/4 of the mushrooms and 3/4 of the
sausage. We don't know Susan's
value system, but we must assume that the three pieces were of equal
value to Susan.
4. What is the value to Bill of the green piece?
5. What is the value to Bill of the yellow piece?
6. What is the value to Bill of the blue piece?
Here's a new copy of the diagram,
in case the original has scrolled off your screen.
Joe likes all three toppings, but he likes mushrooms twice as much as pepperoni and sausage three times as much as pepperoni.
7. What is the value to Joe of the green piece?
8. What is the value to Joe of the yellow piece?
9. What is the value to Joe of the blue piece?
10. Which pieces should Joe bid for, and which pieces should Bill bid for?
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