Apolyton Math Question. bring your calculus hats

[KrazyHorse]

The effect of Si on Sj is lumped into a1 and a2 above

[KrazyHorse]

Originally posted by Lul Thyme
If it does, the argument probably isn't as straightforward.

I don't see why not. If you're in a domain with continuous partial derivatives and no zeroes in any of the partial derivatives anywhere then the absolute minimum (and maximum, of course) on your domain must be at one of the corners.

[KrazyHorse]

Technically, the well-behaved domain here does not include (S1,S2,S3,S4,S5) = (0,0,0,0,0), but we can simply ignore that piece (it's undefined anyway)

[SlowwHand]

That bastard MRT started this thread, then hauled ass, didn't he?

[MRT144]

w=W sorry that was a typo. i realize the optimization for S1,...,S5 is always going to be at the endpoints.

wrt W being fixed do you mean it remains th same through the equation or that it has a constant value?

[KrazyHorse]

I mean, am I allowed to vary it to minimise the function?

[KrazyHorse]

Also, are there any restrictions on x and w? Are both positive?

[KrazyHorse]

In other words, you need to tell me exactly which of those letters I'm allowed to change to minimise the function and which ones I am not.

[MRT144]

Originally posted by KrazyHorse
Also, are there any restrictions on x and w? Are both positive?

you can change w. x is a parameter and is fixed. if i undertand the earlier part correctly.
both are positive. w is a whole niumber. the part of the equation where you 9/w(1+Z) has to be rounded up in all cases to a whole number.

so it seems like we are close to the same page
now. again im really sorry that ive made this so confusing.

[KrazyHorse]

One last thing:

are E1,E2,E3,E4 and E5 parameters or variables?
is Z a parameter or a variable?

[MRT144]

Z is a parameter.
Z={0,.5,1}

E1,...,E5 are parameters. what i was trying to state earlier is that for E1,...,E5 all values of E1,...,E5 are either going to come from the A column, or B column.
a b
E1={60,90}
E2={60,90}
E3={50,74}
E4={40,60}
E5={30,44}

[KrazyHorse]

To summarise:

we wish to minimise the function

T = AC/H with respect to w,S1,...,S5

where

A=(x+((120w)*(S1+S2+S3+S4+S5))
C=ceil(9/(w(1+Z)))
H=(S1*E1+S2*E2+S3*E3+S4*E4+S5*E5)

with x > 0, Z in {0,0.5,1}, E1 in {60,90}, E2 in {60,90}, E3 in {74,50}, E4 in {60,40}, E5 in {44,30} as parameters with the constraints that w is a natural number, S1 is in {0,...,8}, S2 is in {0,...,12}, S3 is in {0,...,16}, S4 is in {0,...,20}, S5 is in {0,...,24}

[MRT144]

Originally posted by KrazyHorse
To summarise:

we wish to minimise the function

T = AC/H with respect to w,S1,...,S5

where

A=(x+((120w)*(S1+S2+S3+S4+S5)))
C=ceil(9/(w(1+Z)))
H=(S1*E1+S2*E2+S3*E3+S4*E4+S5*E5)

with x > 0, Z in {0,0.5,1}, E1 in {60,90}, E2 in {60,90}, E3 in {74,50}, E4 in {60,40}, E5 in {44,30} as parameters with the constraints that w is a natural number, S1 is in {0,...,8}, S2 is in {0,...,12}, S3 is in {0,...,16}, S4 is in {0,...,20}, S5 is in {0,...,24}

yes. this is exactly what i mean. sorry for making it so confusing.

and I just added a parenthesis where it was needed in A. so now it works. I also want to add a function to T so that is always rounds down to a whole number.

[b etor]

[KrazyHorse]

This took about 45 mins. Should work on all 32 bit Windows platforms. Save in some directory. Go to Start>Run>cmd. cd to the directory opt.exe is in. Type in opt, hit enter.

Enter E1, E2, E3, E4, E5, x and Z in order

It will print out the location of the minimum S1, S2, S3, S4, S5 and w, then the value of the minimum.