A firm is considering three projects: Project 1, project 2, and Project 3. Capital requirements and budget limitations in the next three years prevent the firm from undertaking all of these at this time. The net present worth, the capital requirements, and the available funds for the next three years are summarized below: Capital requirements Year 2 $7,000 $8,000 $9,000 $20,000 Year 1 $6,000 $4,000 $5,000 Available funds $12,000 Project 1 Project 2 Project 3 Year 3 $5,500 $6,000 $1,500 $10,000 Net present Worth $22,000 $18,000 $21,000 a) The firm wants to maximize the net present worth of projects undertaken. Formulate the above problem using integer programming problem. b) The firm also would like to consider the following interrelationships among the projects regardless of the funds available : Limit number of selected projects to at most 2. Projects 2 cannot be selected unless both projects 1 and 3 are also selected. Projects 3 must be selected if both projects 1 and 2 are also selected. Represent the above three relationships mathematically.