Thanks. It was an error in the question. Problem solved.
Hello, DooBeeDoo!
They weren't given . . .I can't tell what the right-hand side values of the constraints are.
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 $\displaystyle x$ = number of Product 1 to be produced: .$\displaystyle x \:\geq\:0$
Let $\displaystyle y$ = number of Product 2 to be produced: .$\displaystyle y \:\geq \:0$
I assume they want us to maximize the Profit Function: .$\displaystyle P \:=\:4x + 3y$
We have the following information:
$\displaystyle \begin{array}{cccccccccc}& & \text{Resource 1} &|& \text{Resource 2} &|& \text{Resource 3} &|& \text{Profit} &| \\ \hline \text{Product 1 }(x) &|& 2x &|& x &|& 3x &|& 4x & | \\ \text{Product 2 }(y) &|& 3y &|& 2y &|& 2y &|& 3y &| \\ \hline \text{Available} &|& T_1 &|& T_2 &|& T_3 &|& &| \end{array}$
If we were given $\displaystyle T_1,\:T_2,\:T_3$, we could write the inequalities:
. . $\displaystyle \begin{array}{ccc}x & \geq & 0 \\ y & \geq & 0 \\ 2x + 3y & \leq & T_1 \\ x + 2y & \leq & T_2 \\ 3x +2y & \leq & T_3 \end{array}$
and solve the problem . . .