Linear Programming-Problem

[love_physics]

Hi there!
I have gott a problem with this task. My hope is that someone could help me out of this :=)
we have two products: A and B. There are three moments of processing in order to get the our products:

Number of tools avaible for each moments : 1 1 2
Time to use per day and tool: 8 8 8
Capacity per tool for product A: 500 250 250
Capacity per tool for product B: 200 500 125

The profit made from each manufactured and sold unit of product A is 2,2 $ and from product B is 4,1 $. Because of limitation of market vi can not have more than 1800 of product A and more than 1500 of product B. Number of product B shuld not be less than 20 % of total number of both products.

What shuld I do to maximize the profit?!

I need help the figure out the how to write a LP-program with the problem above.

Can anybody HELP ME with this?!

 

[lippyka]

Thanks a lot in advance!To write an LP-program to maximize the profit with the given parameters, you need to define the variables, identify the objective function, and formulate the constraints. Variables: Let x be the number of units of product A manufactured and sold Let y be the number of units of product B manufactured and sold Objective Function: Maximize 2.2x + 4.1y Constraints: x ≤ 1800 (maximum number of product A) y ≤ 1500 (maximum number of product B) y ≥ 0.2(x + y) (number of product B should not be less than 20% of total number of both products) 8x + 8y ≤ 8*1 (time constraint of the first tool) 8x + 8y ≤ 8*1 (time constraint of the second tool) 500x + 200y ≤ 500*1 (capacity constraint of the first tool for product A) 250x + 500y ≤ 250*1 (capacity constraint of the second tool for product A) 200x + 125y ≤ 125*2 (capacity constraint of the third tool for product B) Therefore, the LP-program is: Maximize 2.2x + 4.1y Subject to: x ≤ 1800 y ≤ 1500 y ≥ 0.2(x + y) 8x + 8y ≤ 8*1 8x + 8y ≤ 8*1 500x + 200y ≤ 500*1 250x + 500y ≤ 250*1 200x + 125y ≤ 125*2 x, y ≥ 0