Remarks & Instructions: There may be more boxes than necessary in any part. Please pay attention to all remarks/instructions and read questions carefully. (a) Constraints: 1. Each constraint should be written into one box. Use the order of decision variables when writing constraints, i.e., in increasing order of indices. Do not put any extra characters or explanations before or after a constraint. Do not scale any constraint. 2. Decision variables should be written in text format, e.g., x1, x2, u11, y1, etc. (similar to Lindo format) but should use the same symbol as the Gams model, without any space between the coefficient, symbol, and indexindices. Also, relations should be in text format (e.g., >= =, -=) 3. Put exactly 1 space before and exactly 1 space after each of the following signs/relations: + (b) Optimal Values: 1. Each optimal numeric value should be written into one box. 2. Do not put any spaces, other/extra characters or explanations other than numeric values. Below are the snapshots of the model and output files of Gams for a mathematical program. Use them to answer the questions next to the snapshots. GAMS MODEL SETS i some set / 1*4/ j some set / 1*3/ PARAMETERS a(i) sone parameter / 1 30, 250, 36, 49 c) some paramater / 1 6, 24, 39/; TABLE b(ij) some table (a) Write the mathematical programming formulations of constraints in Eq1. 1 2 3 1 2 2 2 26 3 2 2 4 4 5 3 3; SCALARS u some scalar / 55 /; VARIABLES z(j) sone variable sone variable y sone variable; y.fx = 0; POSITIVE VARIABLES z; EQUATIONS Eql(i) some equation Eq2 some equation; Eqi(i).. sum(, b[i,j)*z(j)) =G= a(i); Eq2.. sumlj, c(j)*(j)) =E= x; MODEL S2021M /all/: SOLVE 52021M using LP ninimizing x; (b) Write the optimal values of decision variables that are not redundant. Remark: Do not write GAMS OUTPUT symbols, relations, etc. Just give numeric values. **** REPORT SUMMARY : NONOPT INFEASIBLE @ UNBOUNDED Execution 31 VARIABLE X.L = 63.333 some variable 31 VARIABLE y.L = 55.080 some variable 31 VARIABLE Z.L some variable 1 1.667 2 13.333 un Remarks & Instructions: There may be more boxes than necessary in any part. Please pay attention to all remarks/instructions and read questions carefully. (a) Constraints: 1. Each constraint should be written into one box. Use the order of decision variables when writing constraints, i.e., in increasing order of indices. Do not put any extra characters or explanations before or after a constraint. Do not scale any constraint. 2. Decision variables should be written in text format, e.g., x1, x2, u11, y1, etc. (similar to Lindo format) but should use the same symbol as the Gams model, without any space between the coefficient, symbol, and indexindices. Also, relations should be in text format (e.g., >= =, -=) 3. Put exactly 1 space before and exactly 1 space after each of the following signs/relations: + (b) Optimal Values: 1. Each optimal numeric value should be written into one box. 2. Do not put any spaces, other/extra characters or explanations other than numeric values. Below are the snapshots of the model and output files of Gams for a mathematical program. Use them to answer the questions next to the snapshots. GAMS MODEL SETS i some set / 1*4/ j some set / 1*3/ PARAMETERS a(i) sone parameter / 1 30, 250, 36, 49 c) some paramater / 1 6, 24, 39/; TABLE b(ij) some table (a) Write the mathematical programming formulations of constraints in Eq1. 1 2 3 1 2 2 2 26 3 2 2 4 4 5 3 3; SCALARS u some scalar / 55 /; VARIABLES z(j) sone variable sone variable y sone variable; y.fx = 0; POSITIVE VARIABLES z; EQUATIONS Eql(i) some equation Eq2 some equation; Eqi(i).. sum(, b[i,j)*z(j)) =G= a(i); Eq2.. sumlj, c(j)*(j)) =E= x; MODEL S2021M /all/: SOLVE 52021M using LP ninimizing x; (b) Write the optimal values of decision variables that are not redundant. Remark: Do not write GAMS OUTPUT symbols, relations, etc. Just give numeric values. **** REPORT SUMMARY : NONOPT INFEASIBLE @ UNBOUNDED Execution 31 VARIABLE X.L = 63.333 some variable 31 VARIABLE y.L = 55.080 some variable 31 VARIABLE Z.L some variable 1 1.667 2 13.333 un