quadratic

[angel]

hi,

Just wondering if anyone knows how to do Quadratic Programming, i'm attempting some questions but im confused.
So any one know how to do it?

[Ebolamonk3y]

explain this quadratic programming...

[angel]

an example is provided below which will help u understand it:

a shop produces two types of sweet machines A and B. it costs the shop £40 to make each machine A and £70 to make each machine of B.

from research it is suggested that that if the selling price of A and B are set as F and P then they will sell X of A and Y of B and the relationships are given by:
F=£220-3x and P=£250-2Y

Now how would u formulate this problem, the answer u should get is:

-3x^2-2y^2+180X+180Y

[Gokul43201]

What you want to do (assuming reasonable human behavior) is maximize the profit, Pr.
If x of A are produced, and y of B, then the profit is the total selling price, TSP, minus the total cost price, TCP.

Pr = TSP - TCP = TSP(A) - TCP(A) + TSP(B) - TCP(B)
= xF - 40x + yP - 70y, where F and P are as described.

Substituting for F, P, you get

Pr = x(220 - 3x) - 40x +y(250 - 2y) -70y
= 220x - 3x^2 -40x + 250y -2y^2 -70y
= 180x - 3x^2 +180y - 2y^2

That's how you formulate the profit function, which you now want to maximize. The formulation is done the same way as for a LP problem. The difference appears in the function you are optimizing, which is now a quadratic in the variables.

[angel]

thanks alot for that.