Start by making the moment-generating function of this distribution your friend.

Now note that C can be considered a linear function of 100, Y and Y^2. So:

1. E(C) = 100 + 40 E(Y) + 3 E(Y^2).

Get E(Y^2) from the moment generating function of Y - it's the second moment. Or just calculate it directly from the definition - in your case this reduces to finding (use repeated integration by parts).

2. Var(C) = 3^2 Var(Y^2) + 40^2 Var(Y) + 2(3)(40) Cov(Y^2, Y).

Note that Cov(Y^2, Y) = E(Y^3) - E(Y^2) E(Y).

Get E(Y^3) from the moment generating function of Y - it's the third moment. Or just calculate it directly from the definition - in your case this reduces to finding (use repeated integration by parts).

Details are left to you.

Alternativelyyou could just work out the pdf for C and then use it to find E(C) directly from the definition. I'd suggest the method of transformations since the pdf for Y is decreasing in y.

Then finding E(C^2) will enable you to calculate Var(C).