How can the lagrange multipliers in a simple constrained cost minimization problem be calculated? (for binding constraints)

Question

Is there a simple algebric way to calculate the shadow prices (lambda) of the binding constraints given below? This is a cost minimization problem dependent on the generation output. The cost of output dependens on the chosen value for x(1), x(2) and the shape of f(x). The objective function, needed parameters,the result of the optimization problem and also the lambdas are provided below.

Min {b(1)* integral(0,x(1),f(x))+c(1)}+{b(2)*integral(x(1),x(1)+x(2),f(x))+c(2)}
where f(x)=1.25*(1-x)
Parameters
c(1)=0
c(2)=0
b(1)=5
b(2)=15
The constraints
x(1)<=0.2 (?lambda 1)
x(2)<=0.8 (?lambda 2)
x(1)+x(2)>=1
0<=x(1)
0<=x(2)

The result is x(1)=0.2, x(2)=0.8, lambda(1)=32.3169; lambda(2)=22.3169