The Rahway, New Jersey, plant of Metalcase, a manufacturer of office furniture company has depots i=1,....,10 and showrooms j=1......,50. ABC supplies products k=1.....,20 from their depots, sends them to the showrooms to sell in each week t=1...50. Let Xijkt is the non-negative decision variables for the amount of product k sent from depot i to showroom j in week t. a. Express the following as linear constraints using the given decision variables. Amount of product k supplied from depot i in week t cannot exceed sikt b. Express the following as linear constraints using the given decision variables. Demand of showroom j for each product in week t should be at least dikt- c. Express the following as linear constraints using the given decision variables. Total amount of product sent to showroom j in period t cannot exceed 200. d. Determine how many constraints belong to each system defined in parts a, b and c. e. Write expressions for the following systems of constraints in GAMS format 2;&c Xijkt S 1000, Vi,k Constraint1... f. Write the algebraic expressions of the following systems of constraints given in GAMS format. Constraint2(+).. sum((ij,k), X[i,j,k,1))=e=50; The Rahway, New Jersey, plant of Metalcase, a manufacturer of office furniture company has depots i=1,....,10 and showrooms j=1......,50. ABC supplies products k=1.....,20 from their depots, sends them to the showrooms to sell in each week t=1...50. Let Xijkt is the non-negative decision variables for the amount of product k sent from depot i to showroom j in week t. a. Express the following as linear constraints using the given decision variables. Amount of product k supplied from depot i in week t cannot exceed sikt b. Express the following as linear constraints using the given decision variables. Demand of showroom j for each product in week t should be at least dikt- c. Express the following as linear constraints using the given decision variables. Total amount of product sent to showroom j in period t cannot exceed 200. d. Determine how many constraints belong to each system defined in parts a, b and c. e. Write expressions for the following systems of constraints in GAMS format 2;&c Xijkt S 1000, Vi,k Constraint1... f. Write the algebraic expressions of the following systems of constraints given in GAMS format. Constraint2(+).. sum((ij,k), X[i,j,k,1))=e=50