[Binary Integer Programming, 20 points] Catatonic is considering investments for the coming year. They are considering opportunities for new products, product redesigns, and process improvements. Proposals have been solicited from various departments within the firm with estimates of additional profit or cost savings, after expenses, that can be expected in the next three years if the project is selected. Managers have been asked what new investment will be required to launch the projects and their assessment of the likelihood that the profit/savings goal will be realized. The projects are summarized below: Project Profit/Saving Cost Project type Likelihood of success High High $150,000 $165,000 New Redesign $100,000 $60,000 New Redesign Moderate Very high Cat backpack $150,000 Expandable $90,000 airline carrier Catnip clothing $60,000 Cat tree and $80,000 scratching post Cat walking $30,000 harness Automated $40,000 packaging line New supply chain $160,000 IT system $70,000 New Moderate $240,000 High $400,000 Process change Process change Moderate They have a budget of $1,000,000 for New projects. They try to experiment with at least one new product per year and redesign at least one existing product each year. Process change is important with the board of directors and they should make some investment in this area. Although the new packaging line is attractive, it will require the new supply chain IT system to be successful if they select packaging line, they must select IT). Management is risk-averse and does not like to take on more than one moderate risk project (project proponents are notorious with respect to underestimating cost and risk). . The cat backpack and airline carrier serve the same type of buyer. They will introduce at most one of the two. Formulate an IP model that will assist Catatonic in selecting which project to pursue such that profits/savings are maximized while addressing all other restrictions. Do not solve