The students teamed in groups of 4 to solve a case study using methods of linear programming. The students used graphing calculators to analyze the mathematical procedures of these case studies. Palms were used to build PowerPoint presentations and write a final document with their solution to the case studies. A handheld computer hooked to a LCD projector using the MARGI system was used to present their case study solutions. The following are the samples of the case studies used in this process.
Cars and Trucks are made in a factory that is divided into two shops. Shop A performs basic assembly operations, and Shop B performs finishing operations. In shop A it takes 1 person to assemble a truck in 6 days, and 1 person to assemble a car in 3 days. If two people work on that truck, it takes 3 days, 3 people spend 2 days, etc… In shop B it takes one person to finish a truck or a car in 4 days. You have a staff of 18 employees, split over 2 eight-hour shifts. If they worker works in shop A, that same worker cannot work in shop B at a different time during the week. In other words, the worker must stay in the shop that you assign them in from start to finish. You make a profit of $500 per truck, and $350 per car. Split the workers into the shops to maximize the profits over a one week (10 eight hour shifts).
Jetskis and Boats are made in a factory that is divided into two shops. Shop A performs basic assembly operations, and Shop B performs finishing operations. In shop A it takes 1 person to assemble a Boat in 2 days, and 1 person to assemble a jetski in 3 days. If two people work on that Boat, it takes 1 day, 4 people spend 1/2 of a day, etc… In shop B it takes one person to finish a Boat or a jetski in 3 days. You have a staff of 12 employees, split over 2 eight-hour shifts. If they worker works in shop A, that same worker cannot work in shop B at a different time during the week. In other words, the worker must stay in the shop that you assign them in from start to finish. You make a profit of $400 per boat, and $250 per jetski. Split the workers into the shops to maximize the profits over a one week (10 eight hour shifts).
Motorcycles and ATVs are made in a factory that is divided into two shops. Shop A performs basic assembly operations, and Shop B performs finishing operations. In shop A it takes 1 person to assemble a ATV in 4 days, and 1 person to assemble a motorcycle in 6 days. If two people work on that ATV, it takes 2 days, 4 people spend 1 day, etc… In shop B it takes one person to finish a ATV in 2 days or a motorcycle in 3 days. You have a staff of 24 employees, split over 2 eight-hour shifts. If they worker works in shop A, that same worker cannot work in shop B at a different time during the week. In other words, the worker must stay in the shop that you assign them in from start to finish. You make a profit of $400 per ATV, and $300 per motorcycle. Split the workers into the shops to maximize the profits over a one week (10 eight hour shifts).
Sofas and Recliners are made in a factory that is divided into two shops. Shop A performs basic assembly operations, and Shop B performs finishing operations. In shop A it takes 1 person to assemble a recliner in 6 hours, and 1 person to assemble a sofa in 3 hours. If two people work on that recliner, it takes 3 hours, 3 people spend 2 hours, etc… In shop B it takes one person to finish a recliner or a sofa in 4 hours. You have a staff of 18 employees, split over 2 eight-hour shifts. If they worker works in shop A, that same worker cannot work in shop B at a different time during the week. In other words, the worker must stay in the shop that you assign them in from start to finish. You make a profit of $50 per recliner, and $30 per sofa. Split the workers into the shops to maximize the profits over a one week (10 eight hour shifts).
Barbie and Ken Dolls are made in a factory that is divided into two shops. Shop A performs basic assembly operations, and Shop B performs finishing operations. In shop A it takes 1 person to assemble a Barbie in 1/2 hour, and 1 person to assemble a Ken in 1/4 hour. If two people work on Barbie, it takes 1/4 hour, 4 people spend 1/8 hour, etc… In shop B it takes one person to finish a Barbie or a Ken in 1/2 hours. You have a staff of 12 employees, split over 2 eight-hour shifts. If they worker works in shop A, that same worker cannot work in shop B at a different time during the week. In other words, the worker must stay in the shop that you assign them in from start to finish. You make a profit of $8 per Barbie, and $6 per Ken. Split the workers into the shops to maximize the profits over a one week (10 eight hour shifts).