4. [Production Inventory, 36 points) Catatonic wishes to develop a model to assist in scheduling production of its soft-sided cat carriers. These items are made of fabric and have zippered openings to put the cat in the carrier and screened sides to allow the cat to see out. The major labor component is stitching the various pieces of fabric together. Demand for the two most popular models are as follows: Small Medium January 2,000 1,000 February 3,000 1,000 March 4,000 2,000 April 5,000 2,000 It takes 6 minutes to stitch a small carrier and 7 minutes to stitch a medium carrier. Catatonic has 500 hours of stitching time available each month. The cost to make one small carrier is $6.00, but this will increase to $6.20 in April. The cost to make a medium carrier is $7.50, increasing to $7.80 in April. Carriers made one month but not shipped until later, cost Catatonic $0.30 per unit per month in storage and handling costs. This cost is the same for both small and 2 of 3 medium carriers. Catatonic currently has 200 small and 400 medium carriers in inventory and would like to have 500 of each size in inventory at the end of April. Formulate an LP model that will assist Catatonic in deciding how many of each product to make each month such that total costs are minimized. Do not Solve! 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 $150,000 $165,000 Project type Likelihood of success New High Redesign High $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! 4. [Production Inventory, 36 points) Catatonic wishes to develop a model to assist in scheduling production of its soft-sided cat carriers. These items are made of fabric and have zippered openings to put the cat in the carrier and screened sides to allow the cat to see out. The major labor component is stitching the various pieces of fabric together. Demand for the two most popular models are as follows: Small Medium January 2,000 1,000 February 3,000 1,000 March 4,000 2,000 April 5,000 2,000 It takes 6 minutes to stitch a small carrier and 7 minutes to stitch a medium carrier. Catatonic has 500 hours of stitching time available each month. The cost to make one small carrier is $6.00, but this will increase to $6.20 in April. The cost to make a medium carrier is $7.50, increasing to $7.80 in April. Carriers made one month but not shipped until later, cost Catatonic $0.30 per unit per month in storage and handling costs. This cost is the same for both small and 2 of 3 medium carriers. Catatonic currently has 200 small and 400 medium carriers in inventory and would like to have 500 of each size in inventory at the end of April. Formulate an LP model that will assist Catatonic in deciding how many of each product to make each month such that total costs are minimized. Do not Solve! 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 $150,000 $165,000 Project type Likelihood of success New High Redesign High $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