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Problem3(10pts) Consider a seller who sellsmdifferent products. For productj, there areBjunits in inventory. There arencustomers, each customer i is interested in buying a bundle of the productSi, whereSi{1,...,m}and is willing to pay a pricevifor it. For each customer, the seller can only decide to accept his entire requestSior reject him. The objective of the seller is to maximize the revenue. (a). Formulate this problem as an integer program. (b). Consider the following exampleB1=1,B2=2,B3=3,S1={1,2},v1=2,S2={3}, v2=1.S3={1,3},v3=3,S4={2,3},v4=2,S5={2},v5=2. What is the optimal solution to the LP and IP respectively? What is the integrality gap?

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