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In: Statistics and Probability

A company which manufactures canoes employs 120 employees, each of whom working 30 hours per week....

A company which manufactures canoes employs 120 employees, each of whom working 30 hours per week. Half of them work in the carpenter department, 20 persons in the plastics department, and the rest of them at the completion department. The company manufactures the simple canoes with net unit profit € 7 and the luxury canoes with corresponding profit € 10. A simple canoe requires 4.5 hours in the carpenter department and two hours in each of the other two departments. The working hours for each luxury canoe are 5, 1 and 4 at the carpenter department, plastics department and completion department respectively. Marketing calculations have shown that not less than 1/3 and not more than 2/3 of the total number of the canoes should be luxurious. How will the company maximize its overall net profit? Formulate the appropriate LP model.

Expert Solution

Solution:-

Given that

A company which manufactures canoes employs 120 employees, each of whom working 30 hours per week. Half of them work in the carpenter department, 20 persons in the plastics department, and the rest of them at the completion department. The company manufactures the simple canoes with net unit profit € 7 and the luxury canoes with corresponding profit € 10. A simple canoe requires 4.5 hours in the carpenter department and two hours in each of the other two departments. The working hours for each luxury canoe are 5, 1 and 4 at the carpenter department, plastics department and completion department respectively. Marketing calculations have shown that not less than 1/3 and not more than 2/3 of the total number of the canoes should be luxurious.

How will the company maximize its overall net profit? Formulate the appropriate LP model.

Given

Empoyees = 120

Employee working hr per week = 30

Number of employees in each dept

Carpentry = 60

Plastics = 20

Completion = 40

Supply available

Working hrs available at each department = Number of employees in each dept * working hrs available for each employee per week.

Carpentry = 60 * 30 = 1800 hrs

Plastics = 20 * 30 = 600 hrs

Completion = 40 * 30 = 1200 hrs

Unit profit

Simple canoes = 130 pounds

Luxury canoes = 180 pounds

		Hrs required	Hrs required	Hrs required
Unit profit		Carpentry	plastics	completion
Simple canoes	130 pounds	4.5	2	2
Luxury canoes	180 pounds	5	1	4

Hrs available in each department		1800	600	1200

Solution

Number of canoes in each type

Simple canoes = 120

Luxury canoes = 240

Profit = 58800 pounds

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orchestra answered 1 year ago

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