Standard deviation of three producttypes

#1
Hi guys!.
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?