Carl Love

Carl Love

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12 years, 127 days
Himself
Wayland, Massachusetts, United States
My name was formerly Carl Devore.

MaplePrimes Activity


These are answers submitted by Carl Love

Common sense:

  1. Profit = Revenue - Cost  (money in - money out)
  2. Cost = Fixed cost + (cost per unit)*(units sold)
  3. Revenue = units sold * price

Units sold is however a function of price. But it helps here to express price as a function of units sold. Let p be price and x be units sold. The second to fourth sentences of the problem say that

p = 1400-20*(x-13)

Putting it together, we have

Profit = x*(1400 - 20*(x-13)) - (2000 + 1140*x)

limit(sum(1/(n+k), k= 1..n), n= infinity);
                             ln(2)

limit((n!)^(1/n)/n, n= infinity);
                            exp(-1)

d:= binomial(5,2):
mu:= add(min(pair), pair= combinat:-choose(5,2))/d;
                               2
var:= add((min(pair)-mu)^2, pair= combinat:-choose(5,2))/d;
                               1


You'll want the creation command for your Matrix to take account of the sparsity pattern, so use LinearAlgebra:-BandMatrix, like this:

macro(LA= LinearAlgebra):
d:= [$1..80]:
M:= LA:-BandMatrix(
     [(d/4)[5..80], [0$77], (d/2)[3..80], [0$79], 2*d, [0$79], (d/2)[1..78], [0$77], (d/4)[1..76]],
     datatype= float[8]
):

The command that you want is cat, short for "concatenate":

A:= 45:  ExportMatrix(cat("MIN", A, ".txt"), MINM):

You can also use sprintf, short for "string print formatted":

ExportMatrix(sprintf("MIN%d.txt", A), MINM):

You have Digits set to 5. This is often too few digits for fsolve to work with. I changed Digits to 15 for your first failed fsolve, and I got 0.172565524511021. If the extra digits are irrelevant, just truncate them.

Your second failed fsolve is not the same expression as the first!! Nor is it the same as the plotted expression. If I make it the same expression and change the range to 0.3..0.35, I get 0.309465065970785.

Here is the slightly modified worksheet:

Maple_-_Upload.mw

If the goal is some compact Maple code for it, then do

select(isprime, [$1..300]);

If the goal is efficiency, then use a Sieve of Eratosthenes, like this:

N:= 300:
P:= Vector(N, [0], fill=1):
for k from 4 by 2 to N do  P[k]:= 0  end do:
for p from 3 by 2 to isqrt(N) do
     if P[p]=0 then  next  end if;
     for k from p^2 by p to N do  P[k]:= 0  end do
end do:
convert(ArrayTools:-SearchArray(P), list);


(**)

restart:

Possible values of X are 2,3,4,5.

Common denominator:

(**)

d:= binomial(6,2);

15

X=2 can only be made by drawing two 1s.

(**)

P(X=2):= binomial(3,2)/d;

1/5

X=3 can only be made by drawing a 1 and a 2.

(**)

P(X=3):= binomial(3,1)*binomial(2,1)/d;

2/5

X=4 can be two 2s or a 1 and 3.

(**)

P(X=4):= (binomial(2,2)+binomial(3,1)*binomial(1,1))/d;

4/15

X=5 has to be a 2 and 3.

(**)

P(X=5):= binomial(2,1)*binomial(1,1)/d;

2/15

Check that it's a PDF:

(**)

add(P(X=k), k= 2..5);

1

Mean:

(**)

mu:= add(k*P(X=k), k= 2..5);

10/3

Variance:

(**)

var:= add((k-mu)^2*P(X=k), k= 2..5);

8/9

(**)

 


Download probability.mw

This one can be entered into Maple pretty much as it is written above:

restart:
F:= f@g:  f(-1):= 8:  D(f)(-2):= 4:  D(f)(5):= 3:  g(5):= -2:  D(g)(5):= 6:
D(F)(5);
                               24

Diff(5,x):  % = value(%);

Is that good enough?

Note that the last two substitutions cannot be ranked by complexity because the second-to-last has an extra minus sign. These two need to be applied together. This takes about 20 seconds. Then the first eight substitutions can be applied sequentially. This happens almost immediately, and the result is completely substituted and simplified.

For some reason I can't upload the worksheet for display, but it is attached below. 

Download ans_ss.mw

Here's how to use `if` in a plot command. Note that `if` is in single back quotes (accents graves). Also note that there are no parentheses required for your expression.

expr:=
     21430.800231 - x*359.016725 - x/y*389.223603 +
     x*x/y*6.487414 + 118.7333*0.109468
:

plot3d(
     subs(_E= expr, `if`(x/y > 59, undefined, _E)), x= 53..70, y= 1..1.3,
     grid= [20,20], axes= boxed
);

I can't see your commands, but your output is weird: You should never have cos in an algebraic expression not followed by parentheses. And what does fp mean? You may need to do a restart. Here's what I get:

 

(**)

restart:

(**)

H:= (d-1)*cos(f(y))^2+y^2*diff(f(y),y)^2:

(**)

diff(H, y);

-2*(d-1)*cos(f(y))*sin(f(y))*(diff(f(y), y))+2*y*(diff(f(y), y))^2+2*y^2*(diff(f(y), y))*(diff(diff(f(y), y), y))

(**)

combine(%);

-(diff(f(y), y))*d*sin(2*f(y))+(diff(f(y), y))*sin(2*f(y))+2*y*(diff(f(y), y))^2+2*y^2*(diff(f(y), y))*(diff(diff(f(y), y), y))

(**)

simplify(%, size);

(diff(f(y), y))*(2*(diff(diff(f(y), y), y))*y^2+2*(diff(f(y), y))*y-sin(2*f(y))*d+sin(2*f(y)))

(**)

 

It could still be simplified a bit, IMO, but it is very difficult to get Maple to do more.

Download diff.mw

It is normal for some of the parameters to hypergeom to be the empty list [].

Your answer in this case can be converted to another form:

convert(%,  StandardFunctions);

will convert it to a representation in terms of BesselI and GAMMA functions.

 

Also, restart must be spelled in all lowercase letters; Restart does nothing.

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