2-15 please!

o 2-14 Suppose that the decision variables of a mathematical programming model are X a cres of land plot i allocated to crop j in year where i = 1, ..., 47; j = 1, ...,9; t = 1,..., 10. Use summation and for all" indexed notation to write expressions for each of the following systems of constraints in terms of these decision variables, and determine how many constraints belong to each system. (a) The total acres allocated in each year to each plot i cannot exceed the available acres there (call it pi). (b) At least 25% of the total acreage allocated in each of the first 5 years years should be de- voted to corn (crop j = 4). (c) More acres should be devoted to beans (crop j = 1) in each year and each plot than to any other crop. P 2-15 Repeat Exercise 2-14, this time cod- ing the variables and constraints in AMPL as in Table 2.4. 3 Chapter 2 Deterministic Optimization VUU TABLE 2.4 AMPL Model for Pi Hybrids Application 2.2 + identify this as the abstract formulation model section model; + index sets for facilities, hybrids, and regions param 1; param m; param n; set facils :- 1 .. 1; set hybrs := 1 .. m; set regns := 1 .. n; symbolic parameters for facility capacity, buschels per bag, # production costs, regional demands, and shipping costs param uff in facils); param a{h in vars); param pdf in facils, h in hybrs); param d{h in hybrs, r in regns); param sf in facils, h in hybrs, r in regns); # decision variables and types constraints for production and sales var x{f in facils, h in hybrs) >=0; var yff in facils, h in hybrs, r in regns} >= 0; # total cost objective minimize tcost: sum{f in facils, h in hybrs) p[f, h] *x[f, h] + sum{f in facils, h in hybrs, r in regns} sf, h, r]*y[f, h,r]; # main constraint sets for facility capacity, regional demands, + and production-shipping balance subject to fcapf in facils): sum/h in hybrs) a[h] *x[f, h) =0; var yff in facils, h in hybrs, r in regns} >= 0; # total cost objective minimize tcost: sum{f in facils, h in hybrs) p[f, h] *x[f, h] + sum{f in facils, h in hybrs, r in regns} sf, h, r]*y[f, h,r]; # main constraint sets for facility capacity, regional demands, + and production-shipping balance subject to fcapf in facils): sum/h in hybrs) a[h] *x[f, h)