Faldred
DIS Veteran
- Joined
- Dec 18, 2008
Okay, now that we have plan prices, we can play "name that credit's value!".
For the geek-inclined who want to follow the math, stay with me. For everyone else, just ignore it and skip to the end.
Simplifications: I'm rounding plan costs up to the nearest dollar. No one, I hope, will quibble over fractions of a penny. I also value the resort refillable mug (QSDP and DxDP) at $0, because otherwise I'd have to deal with a sliding scale of value based on the length of the stay. Suffice it to say that the mug is simply a "bonus" on these plans beyond the credit values.
Okay, if we make the following variables: C (counter service credit), D (deluxe meal credit), S (snack credit), and T (table service credit), and take the plans as simultaneous equations, we get:
Unfortunately, that's four unknowns and three equations. Not good. But let's turn S from a variable to a constant, which reduces our unknowns by 1. Snack credits are pretty limited in value, and they're the one element all plans have in common, so it makes a good choice for turning into a "constant". Now we are left with 3 unknowns and 3 equations, which will give us meaningful results.
Solving the first and third equations, treating S as a constant, yields:
Now that we know what C is, we can solve the second equation:
Now, all that's left is to plug in whatever value we choose for "S", and we can compute all three variables. Last year, I used $3 as a snack credit value; for 2011, that would yield:
Curiously, changing the value of S affects only C and D. The value of T is constant regardless of what you change S to. (If you expand out the full equation for T, you'll see that you have a +S and a -S, so they cancel out, meaning that T and S are completely independent.)
A CS credit value goes up by the exact amount the snack value drops, and vice-versa. A DxDP meal credit is affected similarly, but scaled by 2/3. So, using different snack credit values, we see:
Similarly, we can solve for child credit values c (child's CS credit), d (child's DxDP meal credit), and t (child's TS credit):
Solving for c and d:
Solving for t, now that we know c:
So, based on out choice of "S", we can determine the values of c and d (since t is a fixed $6.00 value):
Using $3 as the value of a snack credit, the 2011 credit values are:
Note that for the "peak" surcharge, the amount of the surcharge goes directly to the TS credit value, since only the basic DDP is affected and that is the one component that is unique to the basic DDP.
For the geek-inclined who want to follow the math, stay with me. For everyone else, just ignore it and skip to the end.
Simplifications: I'm rounding plan costs up to the nearest dollar. No one, I hope, will quibble over fractions of a penny. I also value the resort refillable mug (QSDP and DxDP) at $0, because otherwise I'd have to deal with a sliding scale of value based on the length of the stay. Suffice it to say that the mug is simply a "bonus" on these plans beyond the credit values.
Okay, if we make the following variables: C (counter service credit), D (deluxe meal credit), S (snack credit), and T (table service credit), and take the plans as simultaneous equations, we get:
Deluxe: 3D + 2S = 79
Basic: 1C + 1T + 1S = 46
QSDP: 2C + 2S = 35
Basic: 1C + 1T + 1S = 46
QSDP: 2C + 2S = 35
Unfortunately, that's four unknowns and three equations. Not good. But let's turn S from a variable to a constant, which reduces our unknowns by 1. Snack credits are pretty limited in value, and they're the one element all plans have in common, so it makes a good choice for turning into a "constant". Now we are left with 3 unknowns and 3 equations, which will give us meaningful results.
Solving the first and third equations, treating S as a constant, yields:
3D = 79 - 2S ==> D = (79 - 2S) / 3
2C = 35 - 2S ==> C = (35 - 2S) / 2
2C = 35 - 2S ==> C = (35 - 2S) / 2
Now that we know what C is, we can solve the second equation:
T = 46 - C - S ==> 46 - ( ( 35 - 2S ) / 2 ) - S
Now, all that's left is to plug in whatever value we choose for "S", and we can compute all three variables. Last year, I used $3 as a snack credit value; for 2011, that would yield:
C = $14.50, T = $28.50, D = $24.33
Curiously, changing the value of S affects only C and D. The value of T is constant regardless of what you change S to. (If you expand out the full equation for T, you'll see that you have a +S and a -S, so they cancel out, meaning that T and S are completely independent.)
A CS credit value goes up by the exact amount the snack value drops, and vice-versa. A DxDP meal credit is affected similarly, but scaled by 2/3. So, using different snack credit values, we see:
S = $4.00 ==> C = $13.50, T = $28.50, D = $23.67
S = $3.00 ==> C = $14.50, T = $28.50, D = $24.33
S = $2.00 ==> C = $15.50, T = $28.50, D = $25.00
S = $1.00 ==> C = $16.50, T = $28.50, D = $25.67
S = $0.00 ==> C = $17.50, T = $28.50, D = $26.33
S = $3.00 ==> C = $14.50, T = $28.50, D = $24.33
S = $2.00 ==> C = $15.50, T = $28.50, D = $25.00
S = $1.00 ==> C = $16.50, T = $28.50, D = $25.67
S = $0.00 ==> C = $17.50, T = $28.50, D = $26.33
Similarly, we can solve for child credit values c (child's CS credit), d (child's DxDP meal credit), and t (child's TS credit):
Deluxe: 3d + 2S = 22
Basic: 1c + 1t + 1S = 12
QSDP: 2c + 2S = 12
Basic: 1c + 1t + 1S = 12
QSDP: 2c + 2S = 12
Solving for c and d:
3d = 22 - 2S ==> d = (22 - 2S) / 3
2c = 12 - 2S ==> c = (12 - 2S) / 2
2c = 12 - 2S ==> c = (12 - 2S) / 2
Solving for t, now that we know c:
t = 12 - c - S ==> 12 - ( ( 12 - 2S ) / 2 ) - S = 6
So, based on out choice of "S", we can determine the values of c and d (since t is a fixed $6.00 value):
S = $4.00 ==> c = $2.00, t = $6.00, d = $4.67
S = $3.00 ==> c = $3.00, t = $6.00, d = $5.33
S = $2.00 ==> c = $4.00, t = $6.00, d = $6.00
S = $1.00 ==> c = $5.00, t = $6.00, d = $6.67
S = $0.00 ==> c = $6.00, t = $6.00, d = $7.33
S = $3.00 ==> c = $3.00, t = $6.00, d = $5.33
S = $2.00 ==> c = $4.00, t = $6.00, d = $6.00
S = $1.00 ==> c = $5.00, t = $6.00, d = $6.67
S = $0.00 ==> c = $6.00, t = $6.00, d = $7.33
Using $3 as the value of a snack credit, the 2011 credit values are:
DxDP Meal Credit: $24.33 adult, $5.33 child
TS Credit: $28.50 ($30.50 peak) adult, $6.00 ($7.00 peak) child
CS Credit: $14.50 adult, $3.00 child
TS Credit: $28.50 ($30.50 peak) adult, $6.00 ($7.00 peak) child
CS Credit: $14.50 adult, $3.00 child
Note that for the "peak" surcharge, the amount of the surcharge goes directly to the TS credit value, since only the basic DDP is affected and that is the one component that is unique to the basic DDP.