Exercise in Indexing (exer-sum)

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Problem

Given are

P_j = , A_i = , X_i,j = and Y _i,j =

Evaluate a) – d) by hand, write the first 4 terms of the sum expansion for e) – g).

a) ∑ _i=1⁵A _i b) ∑ _j=1⁴P _j c) ∑ _i=1⁵X _i,j for j = 1 d) ∑ _j=1⁴X _i,j for i = 1…2

e) ∑ _i=1⁵ ∑ _j=1⁴X _i,j ⋅ Y _i,j f) ∑ _i=1⁵ ∑ _j=1⁴P _j ⋅ X_i,j g) ∑ _i=1⁵A _i ⋅ Y _i,j for j = 1…4

Implement it in LPL

a) Write an LPL-code which defines two sets i and j for the indices and the vector and matricies from Problem as parameters. Display all data with Writep() statements.

Install LPL on your computer. Alternatively you can enter the models directly online at empty. Make sure you save your models on your computer by copy/pasting your code to a local file.

b) Write LPL-code to compute and display all sums from the problem. We give two examples:

  Write(' %5.2f' n', sum' {i' } A); 
    Write(' %s' n', {i|i<=2} Format('i=%d: %5.2f   ',i,sum{j} X));

Solution

model exerSum "Exercise in Indexing"; 
    set i:=1..5; 
    set j:=1..4; 
    parameter P{j}:=[4 6 8 7]; 
    parameter A{i}:=[5,2,2,4,1]; 
    parameter X{i,j}:=[3 6 5 4, 6 7 7 1, 7 8 4 2, 3 3 2 6, 5 8 3 8]; 
    parameter Y{i,j}:=[4 1 6 6, 3 3 4 4,  4 8 5 3, 6 7 4 5, 3 5 5 3]; 
    Writep(P,A,X,Y); 
    Write('a) %5.2f' n', sum{i} A); 
    Write('b) %5.2f' n', sum{j} P); 
    Write('c) %5.2f' n', sum{j} X[1,j]); 
    Write('d) %s' n', {i|i<=2} Format('i=%d: %5.2f   ',i,sum{j} X)); 
    Write('e) %5.2f' n', sum{i} sum{j} X[i,j]*Y[i,j]); 
    Write('f) %5.2f' n', sum{i} sum{j} P[j]*X[i,j]); 
    Write('g) %s' n', {j} Format('j=%d: %5.2f   ',j, sum{i} A[i]*Y[i,j])); 
  end

References