ISE $362$ PS $9$: Location and Distribution Decisions in Supply Chains $12/12/2023$Question $1$:Consider a supplier order allocation problem under multiple sourcing, where buying $2500$ units of a certain product from three different suppliers is required. The fixed setup cost $($independent of the order quantity$),$ variable cost $($unit price$),$ and the maximum capacity of each supplier are given in the table below.The objective is to minimize the total cost of purchasing $($fixed plus variable cost$).$ Supplier$123$Fixed Cost$ $150$$ $250$ $ $450$Capacity$900$ units$1400$ units $700$ unitsUnit Price$ $12/$ unit for the first $400$ units$ $6/$ unit for the remaining $500$ units $ $8/$ unit for the first $600$ units$ $5/$ unit for the remaining $800$ units $ $3/$ unit for all $700$ units a$)$ Formulate this as a linear integer programming problem. You must define all your variables clearly, write out the constraints to be satisfied with a brief explanation of each, and develop the objective function.b$)$ Reformulate the problem under the assumption that both suppliers $1$ and $2$ offer all units discount, as described in the following:i$)$ Supplier $1$ charges $$12/$unit for orders up to $400$ units; for orders more than $400$ units, the entireorder will be priced at $$6/$unit$.$ii$)$ Supplier $2$ charges $$8/$unit for orders up to $600$ units; for orders more than $800$ units, the entireorder is priced at $$5/$unit$.$Question $2$:Explain how the following conditions can be represented as linear constraints using binary variables.a$)$ Either$1+23$or$1+4210$b$)$ Variable $2$ can assume values $0,4,7,10,$ and $12$ onlyc$)$ If $23,$ then $36$; Otherwise $34($assume $2$ and $3$ are integers$)$d$)$ At least $2$ out of the following $5$ constraints must be satisfied:$1+2712321+32201321026,1,20$