Help with formulating a linear programming problem

Help with formulating a linear programming problem

I have the following linear programming problem I would like to be verified:

I have sketched the problem in the following picture:

Here is my attempted solution:
I figured that I have ten variables (corresponding to the colored lines,
between each building): $x_1, x_2, ..., x_{10}$ which are the amounts (in
tons) of raw materials from Source 1 --> Plant A, Source 1 --> Plant B,
Source 2 --> Plant A, Source 2 --> Plant B, Plant A --> Market 1, Plant A
--> Market 2, ............, Plant B --> Market 3.
The formulation I get is the following:
$$\text{minimize}\;\;\; 1x_1 + 1.5x_2 + 2x_3 + 1.5x_4 + 4x_5 + 2x_6 + 1x_7
+ 3x_8 + 4x_9 + 2x_{10}$$ $$\text{subject to}\;\;\;x_1 + x_2 = 10$$
$$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x_3 + x_4 = 15$$
$$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x_5 + x_8 = 8$$
$$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x_6 + x_9 = 14$$
$$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x_7 + x_{10} = 3$$
$$\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;x_1 \ge 0, x_2 \ge 0, \cdots, x_{10}
\ge 0.$$
I would appreciate if someone could verify the correctness of my answer :)
Thank you for any help!