Five players are dividing a cake among themselves using the lone-divider method. After the divider D cuts the cake into five slices ( s 1 , s 2 , s 3 , s 4 , s 5 ) the choosers C 1 , C 2 , C 3 , and C 4 submit their bids for these shares. a. Suppose that the choosers’ bid lists are C 1 : { s 2 , s 3 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 1 , s 2 } ; C 4 : { s 1 , s 3 , s 4 } Describe three different fair divisions of the land. Explain why that’s it—why there are no others. b. Suppose that the choosers bid lists are C 1 : { s 1 , s 4 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 2 , s 4 , s 5 } ; C 4 : { s 2 } Find a fair division of the cake. Explain why that’s it—there are no others.
Five players are dividing a cake among themselves using the lone-divider method. After the divider D cuts the cake into five slices ( s 1 , s 2 , s 3 , s 4 , s 5 ) the choosers C 1 , C 2 , C 3 , and C 4 submit their bids for these shares. a. Suppose that the choosers’ bid lists are C 1 : { s 2 , s 3 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 1 , s 2 } ; C 4 : { s 1 , s 3 , s 4 } Describe three different fair divisions of the land. Explain why that’s it—why there are no others. b. Suppose that the choosers bid lists are C 1 : { s 1 , s 4 } ; C 2 : { s 2 , s 4 } ; C 3 : { s 2 , s 4 , s 5 } ; C 4 : { s 2 } Find a fair division of the cake. Explain why that’s it—there are no others.
Solution Summary: The author explains the three fair divisions of the land using the lone-divider method.
Five players are dividing a cake among themselves using the lone-divider method. After the divider
D
cuts the cake into five slices
(
s
1
,
s
2
,
s
3
,
s
4
,
s
5
)
the choosers
C
1
,
C
2
,
C
3
, and
C
4
submit their bids for these shares.
a. Suppose that the choosers’ bid lists are
C
1
:
{
s
2
,
s
3
}
;
C
2
:
{
s
2
,
s
4
}
;
C
3
:
{
s
1
,
s
2
}
;
C
4
:
{
s
1
,
s
3
,
s
4
}
Describe three different fair divisions of the land. Explain why that’s it—why there are no others.
b. Suppose that the choosers bid lists are
C
1
:
{
s
1
,
s
4
}
;
C
2
:
{
s
2
,
s
4
}
;
C
3
:
{
s
2
,
s
4
,
s
5
}
;
C
4
:
{
s
2
}
Find a fair division of the cake. Explain why that’s it—there are no others.
3. Let
sin (22) + cos (T2)
f(z) =
z(22 + 1)(z+1)
Compute f(z)dz over each of the contours/closed curves C1, C2, C3 and C4 shown
below.
L
10
-C
x
Don't use any Al tool
show ur answer
pe
n and paper then take
what is the slope of the linear equation-5x+2y-10=0
1. Evaluate
(2,5)
(3x+y)dx+(2y-x)dy
(0,1)
(i) along the straight lines from (0, 1) to (2, 1) and then from (2, 1) to (2,5), and (ii)
along the parabola y = x² + 1.
Don't use any Al tool
show ur answer in pe
n and paper then take
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