Northwest Manufacturing assembles heavy duty materials handling carts to meet quarterly demands. Elementary components, which consist of wheels, steering yokes, and carrying platforms, are first assembled separately. Then each steering yoke is equipped with 4 wheels to form the front-end subassembly. Finally, front-end subassemblies are combined with a carrying platform and 8 additional wheels at the rear to complete the cart. Components, subassemblies, and finished carts produced in any quarter may be used or shipped in the same quarter or held over as inventory. Northwest seeks a plan that minimizes inventory holding costs while meeting demand and respecting the factory production capacity. The sets and parameters of an AMPL model for this problem have been defined as follows:set ELEMENTS;# elementary components, subassemblies,# and final productparam Q integer > 1;# number of quarters being modeledparam time {ELEMENTS} >= 0;# estimated factory assembly time# (in hours) to produce each elementparam hours_avail > 0;# total production hours available# per quarterparam needed {ELEMENTS, ELEMENTS} >= 0;# needed[d, e] is the number of units# of element d needed to make # 1 unit of element eparam demand {ELEMENTS,1..Q} >= 0;# quarterly demand for each element.# if e is cart, demand[e, q] is number # of carts required each quarter; # otherwise, demand[e, q] = 0.param initial_hold {ELEMENTS} >= 0;# total units in inventory at the start# of the 1st quarterThere are three collections of decision variables:var Prod {ELEMENTS,1..Q} >=0; # number of each element# produced in each quartervar Use {ELEMENTS,1..Q} >=0; # number of each element used each quarter# to produce other elementsvar Hold {ELEMENTS,0..Q} >=0; # number of each element held in inventory# at the end of each quarterHere is a collection of data for this model:set ELEMENTS := yoke wheel platform front-end cart ; param Q := 4 ;param:value time initial_hold :=yoke120 0.06 200wheel 40 0.07 200platform 75 0.04 200front-end400 0.12 200cart700 0.32 200 ;param hours_avail := 1150 ; param needed: yoke wheel platform front-end cart :=yoke00010wheel00048platform00001f ront-end00001cart00000 ;param demand: yoke wheel platform front-end cart :=1 00005002 000012003 000010004 0000300 ;The following questions ask you to write some constraints for this model. (We will skip the objective.) The parameters are used roughly in the order in which they appear above. a: Complete the following AMPL constraints that, in each quarter q, total hours used for production must not exceed total hours available:subject to HoursAvail {q in 1..Q}: sum {e in ELEMENTS}b: Complete the following AMPL constraints that, for each element e in each quarter q, the units of element e used to produce other elements equals the sum over all elements f of the units of e needed in producing f. subject to DefineUse {e in ELEMENTS, q in 1..Q}:Use[e, q] = sum {f in ELEMENTS}c: Complete the following AMPL constraints that, for each element e in each quarter q, the units of element e produced in the quarter plus units of e held from the previous quarter equals units of e used in making other elements during the quarter plus units of e held at the end of the quarter plus demand for e. subject to Balanced: Complete the following AMPL constraints that, for each element e, the amount held at the end of quarter 0 is equal to the initial inventory available. subject to InitHoldThe following questions ask about the numbers of constraints and variables of various kinds in the linear program specified by the above model and data:e: How many HoursAvail constraints are in the linear program? How many variables appear in each HoursAvail constraint?f: How many DefineUse constraints are in the linear program?g: How many InitHold constraints are in the linear program? How many variables appear in each InitHold constraint?