Question

could someone explain how to formulate a linear programming problem? really hate decision maths :(

Answer 1

For example:


"The Elves toy company makes toy trains and dolls' prams, which use the same wheels and logo stickers.

Each train requires 8 wheels and 2 logo stickers

Each prain requires 8 wheels and 3 logo stickers

The company has 7200 wheels and 2200 logo stickers available.

The company is to make at least 300 of each type of toy and at least 800 toys in total.

The company sells each train for £20 and each pram for £25.

The company makes and sells x trains and y prams."

Answer 2

help :(

Answer 3

Money made or revenue is objective function
R = 20x + 25y
constraints:
x>=300
y>=300
x+y >=800
---> y>=800-x
8x+8y<= 7200
---> y <=900 - x
2x+3y <= 2200
---> y<=2200/3 - (2/3)x

Answer 4

graph all the constraints
then evaluate at the points along outside of bounded shaded area by substituting the points into objective function

Answer 5

Hi yes but how do you formulate it from the wording? I get really confused on how to do that. :(

Answer 6

I didnt get how you got:
x>=300 y>=300 x+y >=800

---> y <=900 - x
---> y <=900 - x

:S

Answer 7

ok yes sorry i was away for a bit there

x>=300 y>=300, x+y >=800
This comes from statement
The company is to make at least 300 of each type of toy and at least 800 toys in total.
x refers to number of trains made
if you have make at least 300, then num trains made must be greater or equal to 300
hence x>=300
same logic for y>=300 , y refers to num of prams made
total toys made refers to adding x and y and together they must be greater or equal to 800
hence x+y>=800

Answer 8

8x+8y<= 7200
---> y <=900 - x
2x+3y <= 2200
---> y<=2200/3 - (2/3)x

These come from statement:
Each train requires 8 wheels and 2 logo stickers Each prain requires 8 wheels and 3 logo stickers The company has 7200 wheels and 2200 logo stickers available.

The num of trains is x and num of prams is y
Each toy has 8 wheels right?
so num of wheels is 8 times num of toys -->8*(x+y)
since there only 7200 wheels
num wheels <= 7200 or 8x+8y <=7200
here i solved for y by subtracting 8x and dividing by 8
hence y <=900-x
same logic for stickers
num stickers <= 2200
but there are 2 on each train and 3 on each pram so num of stickers equals 2x+3y
solve for y by subtracting 2x and dividing by 3
hence y<=2200/3 - (2/3)x

Answer 9

hope that make it more clear

Answer 10

oh so you know the variables, are you comparing them against each other? Like the wheel against the wheel as there is a total for wheels?