Question.1 Develop a GAMS code to solve the Farmer lones" optimization problem: maxz=100x1+30x2s.f.x1+x2710x1+4x24010x230x1,x20 1. Submit your GAMS code. 2. Determine the optimal solution x1,x2,z (compare it with the graphical solution found in Lecture 2). 3. Find the shadow price of the first constraint, and explain the results. 4. Find the shadow price of the second constraiat, and explain the results. Question 2 Develop a GAMS code to solve the golf bags optimization problem: max10m+9Ds.7/10S+D6301/2S+5/6D600S+2/3D7081/10S+1/4D135S,D0 1. Submit your GAMS code (only for the original case 1). Case 1: Nochanges in Parameters: 2. Determine the optimal solution S, D, OFV (comsare it with the graphical solution found in Lecture 3). 3. Find the shadow price of the first constraint, and explain the results. (compare it with the shadow price of same constraint found in Lecture 3). Case 2: Changing Obiective Function Coefficients: 4. Re-solve the problem with changing the S and D coefficients in objective function to 13 and 14 , respectively (within the allowable range). Then find the solution of optimization problem S,D, ofV and compare it with results ia step 2 above. 5. Re-solve the problent with changing the S and D coefficient in ebjective function to 16 and 17 , respectively (outside the allowable range). Then find the solution of optimization problem S, D, 0FV and compare it with results in step 2 and step 4 above. Case 3: Changing RHS of a Constraint: 6. Re-solve the problem with changing the RHS of first censtraint to 682 (within allowable range). Then find how much is the shadow price of the constraint. 7. Re-solve the problem with changing the RHS of first constraint to 700 (exceeding the upper bound limit of RHS). Then find how much is the new shadow price of the constraint. Question 3 Develop a GAMS code to solve the Job Sequencing (IP) optimization problem minz=(x14+30)+(x24+18)+(x33+28)s.t.x13xII+20x14x13+25x22x21+15x24x22+20x33x32+35x1l+20x2lMylx21+15xuM(1y1)x22+20x32My2x32+35x22M(1y2)x13+25xi3My2xug+28xisM(1yj)x14+30x24My1x24+18x14M(1y4)xij0fori=1,2,3;j=1,2,3,4yi=0or1 M is a large number 1. Submit your GAMS code. 2. Determine the optimal solution of all variables and the objective function value