1) A car manufacturer has an assembly line that can be used to assemble two different types of cars: a sedan and a wagon. If the assembly line is dedicated to production of one or the other type of car, the potential throuhput of cars is a maximum of 90 sedans or 120 wagons per day. A mix of sedans and wagons is allowable.
Assume that it takes no time to convert the production line from one type of car to the other. There is currently a shortage of tires, so that not more than 110 vehicles of either type can be assembled per day. The manufacturer also has to meet contracts to supply 33 sedans and 20 wagons per day. Prodcution above these levels is at the discretion of the maufacturer.
If profit per car is $1800 per sedan and $1500 per wagon, set up an LP matrix to select the profit maximizing combination of cars.
2) A company uses both radio and television advertisements to promote its product. A radio advertisement costs $100 and, on average, generates sales of 20 additional units of the product. A television advertisement costs $700 and generates extra sales of 150 units.
The only radio station in town has a policy of not allowing an advertisement to be played more than once a day. There is a contract with the only television station in town to run at least two advertisements per month. The budget for advertising in september is $4200.
Formulate an LP matrix to maximize the number of extra sales generated thru advertising in September.
3) With one week to go, a student wishes to minimize the number of hours spent studying for three exams: one each for mathematics, history, and literature.
Suppose that with no further study, the student would score 40 for mathematics, 30 for history, and 45 for literature. Each hour of study would improve these marks by 1 mark, 2 marks, and 0.5 mark, respectively. To pass a particular course the student must score at least 70 in mathematics and 50 each in history and literature. In addition, the total combined score of the three units must be at least 185.
Set up an LP matrix to minimize study effort.
Assume that it takes no time to convert the production line from one type of car to the other. There is currently a shortage of tires, so that not more than 110 vehicles of either type can be assembled per day. The manufacturer also has to meet contracts to supply 33 sedans and 20 wagons per day. Prodcution above these levels is at the discretion of the maufacturer.
If profit per car is $1800 per sedan and $1500 per wagon, set up an LP matrix to select the profit maximizing combination of cars.
2) A company uses both radio and television advertisements to promote its product. A radio advertisement costs $100 and, on average, generates sales of 20 additional units of the product. A television advertisement costs $700 and generates extra sales of 150 units.
The only radio station in town has a policy of not allowing an advertisement to be played more than once a day. There is a contract with the only television station in town to run at least two advertisements per month. The budget for advertising in september is $4200.
Formulate an LP matrix to maximize the number of extra sales generated thru advertising in September.
3) With one week to go, a student wishes to minimize the number of hours spent studying for three exams: one each for mathematics, history, and literature.
Suppose that with no further study, the student would score 40 for mathematics, 30 for history, and 45 for literature. Each hour of study would improve these marks by 1 mark, 2 marks, and 0.5 mark, respectively. To pass a particular course the student must score at least 70 in mathematics and 50 each in history and literature. In addition, the total combined score of the three units must be at least 185.
Set up an LP matrix to minimize study effort.
