# Thread: Generating a Linear Programming problem

1. ## Generating a Linear Programming problem

Thanks. It was an error in the question. Problem solved.

2. Hello, DooBeeDoo!

I can't tell what the right-hand side values of the constraints are.
They weren't given . . .
And without them, we can't write the constraints (exactly).

A company manufactures two products from three scarce resources.
The net profits are 4 and 3, respectively.

Each unit of Product 1 uses 2 units of Resource1, 1 unit of Resource 2, and 3 units of Resource 3.

Each unit of Product 2 uses 3 units of Resource 1, 2 units of Resource 2, and 2 units of Resource 3.

Let $x$ = number of Product 1 to be produced: . $x \:\geq\:0$
Let $y$ = number of Product 2 to be produced: . $y \:\geq \:0$

I assume they want us to maximize the Profit Function: . $P \:=\:4x + 3y$

We have the following information:

$\begin{array}{cccccccccc}& & \text{Resource 1} &|& \text{Resource 2} &|& \text{Resource 3} &|& \text{Profit} &| \\ \hline \text{Product 1 }(x) &|& 2x &|& x &|& 3x &|& 4x & | \\ \text{Product 2 }(y) &|& 3y &|& 2y &|& 2y &|& 3y &| \\ \hline \text{Available} &|& T_1 &|& T_2 &|& T_3 &|& &| \end{array}$

If we were given $T_1,\:T_2,\:T_3$, we could write the inequalities:

. . $\begin{array}{ccc}x & \geq & 0 \\ y & \geq & 0 \\ 2x + 3y & \leq & T_1 \\ x + 2y & \leq & T_2 \\ 3x +2y & \leq & T_3 \end{array}$

and solve the problem . . .