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A cheese firm produces two types of cheese: swiss cheese and sharp cheese. The firm has 60 experienced workers and would like to increase its working force to 90 workers during the next eight weeks. Each experienced worker can train three new employees in a period of two weeks during which the workers involved virtually produce nothing. It takes one man-hour to produce 10 pounds of Swiss cheese and one man-hour to produce 6 pounds of sharp cheese. A work week is 40 hours. The weekly demands (in 1000 pounds) are summarized below: WEEK CHEESE TYPE Swiss cheese Sharp cheese 1 2 3 11 12 13 8 4 5 6 7 8 18 14 18 20 20 10 8 12 13 12 12 8 Suppose that a trainee receives the same full salary as an experienced worker. Further suppose that overaging destroys the flavor of the cheese, so that inventory is limited to one week. How should the company hire and train its new employees so that the labor cost is minimized over this 8-week period? Formulate the problem as a linear program.

A cheese firm produces two types of cheese: swiss cheese and sharp cheese. The firm has 60 experienced workers and would like to increase its working force to 90 workers during the next eight weeks. Each experienced worker can train three new employees in a period of two weeks during which the workers involved virtually produce nothing. It takes one man-hour to produce 10 pounds of Swiss cheese and one man-hour to produce 6 pounds of sharp cheese. A work week is 40 hours. The weekly demands (in 1000 pounds) are summarized below: WEEK CHEESE TYPE Swiss cheese Sharp cheese 1 2 3 11 12 13 8 4 5 6 7 8 18 14 18 20 20 10 8 12 13 12 12 8 Suppose that a trainee receives the same full salary as an experienced worker. Further suppose that overaging destroys the flavor of the cheese, so that inventory is limited to one week. How should the company hire and train its new employees so that the labor cost is minimized over this 8-week period? Formulate the problem as a linear program.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A cheese firm produces two types of cheese: swiss cheese and sharp cheese. The firm has 60 experienced workers and would like to increase its working force to 90 workers during the next eight weeks. Each experienced worker can train three new employees in a period of two weeks during which the workers involved virtually produce nothing. It takes one man-hour to produce 10 pounds of Swiss cheese and one man-hour to produce 6 pounds of sharp cheese. A work week is 40 hours. The weekly demands (in 1000 pounds) are summarized below: WEEK 4 5 6 7 8 CHEESE TYPE Swiss cheese Sharp cheese 1 2 3 11 12 13 8 10 14 18 20 20 18 8 12 13 12 12 8 Suppose that a trainee receives the same full salary as an experienced worker. Further suppose that overaging destroys the flavor of the cheese, so that inventory is limited to one week. How should the company hire and train its new employees so that the labor cost is minimized over this 8-week period? Formulate the problem as a linear program.
Transcribed Image Text:A cheese firm produces two types of cheese: swiss cheese and sharp cheese. The firm has 60 experienced workers and would like to increase its working force to 90 workers during the next eight weeks. Each experienced worker can train three new employees in a period of two weeks during which the workers involved virtually produce nothing. It takes one man-hour to produce 10 pounds of Swiss cheese and one man-hour to produce 6 pounds of sharp cheese. A work week is 40 hours. The weekly demands (in 1000 pounds) are summarized below: WEEK 4 5 6 7 8 CHEESE TYPE Swiss cheese Sharp cheese 1 2 3 11 12 13 8 10 14 18 20 20 18 8 12 13 12 12 8 Suppose that a trainee receives the same full salary as an experienced worker. Further suppose that overaging destroys the flavor of the cheese, so that inventory is limited to one week. How should the company hire and train its new employees so that the labor cost is minimized over this 8-week period? Formulate the problem as a linear program.
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