Simplex Lp interpretation of dual problem´s solution

I am wondering whether my interpretation of my simplex dual problem result is correct.

The primal problem is:

                                M1  M2  M3  M4
    materialdemand for 1 kg P1  0   2   1   4
    materialdemand for 1 kg P2  3   2   2   0
    materialdemand for 1 kg P3  1   2   1   1
    constraint          (kg)    220 295 240 120

*Mi = material; Pi = product

    Z= 2,3X1 + 2,3X2 + 2X3 --> max

Constraints:

3X2 +   X3 <= 220
2X1 + 2X2 + 2X3 <= 295
X1 + 2X2 +  X3  <=240
4X1 + X3 <=120
X1;X2;X3 >= 0

the dual problem is the as follows:

V = 220w1 + 295w2 + 240w3 + 120w4 --> min

Constraints:

2W2 +   W3 + 4W4 >= 2,3
3W1 + 2W2 + 2W3 >= 2,3
W1 + 2W2 +   W3 +   W4  >=2
W1;W2;W3;W4 >= 0

I interpret w1 in my final tableau being the opportunity costs of M1, W2 of M2, W3 of M3 and W4 of M4.

I would appreciate if you could help 🙂