Using Excel to Maximize Multi-Variable Equation

I am not sure how to bets attack this problem without countless hours of trial and error. Hoping some expertise and Excel can help.

I have 14 variables that I need to add together in order to maximize the sum. The 14 variables cannot add up to over 100 and each variable has a different weight it contributes towards the sum.

For example, I know that 16,0,5,9,5,9,7,7,7,7,7,4,10,9 = .46 and 0,0,0,0,0,20,0,0,20,20,0,20,20,0 = -.08. I could provide thousands of more patterns their their sums based on trail and error, but I am trying to save time and effort.

How can I go about trying to figure out which sequence of numbers will yield the highest sum? Is this a way Excel, or another free resource, can help?

Weights are approximately as follows:

A = 3.29
B = -3.15
C = .66
D = 4.64
E = -.94
F = 5.53
G = -.44
H = -2.24
I = 1.91
J = -1.41
K = .36
L = .38
M = -.50
N = -2.19

I think the weight may change when used in different combinations. But for simplicity, solving the equation with the above weights should get my closer to a result.