I need some statistics help here.

I have three producttypes;

Plates, spoons and mugs

This is what i know

Spoons:

Mean = 565,87

Variance = 50677,28

Standard Deviation = 225,12

Correlation with plates= 0,8394

Correlation with mugs = 0,8271

Plates:

Mean = 1806,83

Variance = 299886,53

Standard Deviation = 547,62

Correlation with spoons= 0,8394

Correlation with mugs = 0,9571

Mugs:

Mean = 2520

Variance = 608400

Standard Deviation = 780

Correlation with plates = 0,9571

Correlation with spoons= 0,8271

I've calculated that the mean of the three producttypes combined (The sum of all producttypes) Plates_mean + Spoons_mean + Mugs_Mean = 565,87 + 1806,83 + 2520 = 4892,7

How do I find the standard deviation of the sum of all producttypes combined?