5. (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 Cat backpack $150,000 $150,000 New High Expandable $90,000 $165,000 Redesign High airline carrier Catnip clothing $60,000 $100,000 New Moderate Cat tree and $80,000 $60,000 Redesign Very high scratching post Cat walking $30,000 $70,000 New Moderate harness Automated $40,000 $240,000 Process High packaging line change New supply chain S160,000 $400,000 Process Moderate IT system change 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 ). 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