can someone?

Cans omeone help me with this one?




Maximize

P = 40x1 + 60x2 + 50x3

Subject to the constraints

2x1 + 2x2 + x3 < 8
X1 – 4x2 + 3x3 < 12

X1 > 0 X2 > 0 X3 > 0

P = 40x1 + 60x2 + 50x3 = 40x + 120x + 150x = 310x
max = infinity

Unless you mean 40x^1 + 60x^2 + 50x^3 in whichcase:
dx/dy(x^n )= nx^n
dx/dy(50x^3 + 60x^2 + 40x) = 150x^2 + 120x + 40

maximums and minimums are at:
150x^2 + 120x + 40 = 0
15x^2 + 12x + 4 = 0
x = (-12 +- sqr(12^2 - 4*15*4))/2*15 = -12/30 +- sqr(144-240)/30
= -2/5 +- i*sqr(96)/30 = -2/5 +- i*4*sqr(6)/30 = -2/5 +- 2i*sqr(6)/15
= -2/5 + .326i or -2/5 - .326i

The answer is imaginary.

i think they mean there are three variables:

x₁, x₂ and x₃

In that case, there is a simple algorithm that solves all these things for you, I think it's even call SIMPLEX, just search for it, and you'll probably be able to find a program that solves them for you.

Well then why in the world didn't he just use x, y and z??? :confused:

Hello:
This simple visual basic probabilistic program can solve your problem:

Code:

---

RANDOMIZE
pmax=-1e30
FOR i=1 TO 10000
  ' random digits in the range 0-8
  x1=INT(8*RND)
  x2=INT(8*RND)
  x3=INT(8*RND)
  ' test the inequalities
  IF 2*x1+2*x2+x3<8 AND x1-4*x2+3*x3<12 THEN
      ' calculate p
      p=40*x1+60*x2+50*x3
      ' is better?
      IF p>pmax THEN
        pmax=p
        PRINT x1, x2, x3, pmax
      END IF
  END IF
NEXT i

---

The solution is x1=0, x2=1, x3=5 and the maximum is 310
If you wish real numbers rather than integer numbers, remove the "INT" in the code.
Regards

Quote:

---

Originally posted by MarcoA
Hello:
This simple visual basic probabilistic program can solve your problem:

Code:

---

RANDOMIZE
pmax=-1e30
FOR i=1 TO 10000
  ' random digits in the range 0-8
  x1=INT(8*RND)
  x2=INT(8*RND)
  x3=INT(8*RND)
  ' test the inequalities
  IF 2*x1+2*x2+x3<8 AND x1-4*x2+3*x3<12 THEN
      ' calculate p
      p=40*x1+60*x2+50*x3
      ' is better?
      IF p>pmax THEN
        pmax=p
        PRINT x1, x2, x3, pmax
      END IF
  END IF
NEXT i

---

The solution is x1=0, x2=1, x3=5 and the maximum is 310
If you wish real numbers rather than integer numbers, remove the "INT" in the code.
Regards

---

int(8*rnd) returns a random number between 0 and 7, not 0 and 8.
also, it would make more sense to just loop x1, x2 and x3 through all the values of 8. It totals up to 512 iterations MAX.