Please show all the steps

Question (2) 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 Year 1 Year 3 Net present Worth Project 1 Project 2 Project 3 Available funds $6,000 $4,000 $5,000 $12,000 $7,000 $8,000 $9,000 $20,000 $5,500 $6,000 $1,500 $10,000 $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. Proi