# Linear Programming

Subject: Linear Programming

Details: The programs that can be used are Excel Slover, Data analyis, spreed sheets, linear Programming and PERT/CPM models.

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19. A company that makes garments is unionized. Each full time employee works 40 hours per week,earns $13 per hour, and the union contract says that the number of full time employees can never drop below 20. Nonunion part time employees can be hired, but there must be at least 2 full time employees for each part time employee, and part time employees can work no more than 20 hours per week. They make $10 per hour. The company has 5,000 square feet of material available each week. The cost of this material is reflected in the Gross Profit per garment (but the cost of labor is not included in that cost). Fabrication requirements are as follow:

Product Material Required Labor Required Gross Profit per garment

A 2 square feet 30 minutes $8

B 1.5 square feet 45 minutes $10

C 1 square feet 40 minutes $6

Maximize the company's net profit: gross profit minus the cost of labor.

20. A Computer Center must have the following minimum number of consultants on duty during each 4-hour period:

8 AM to Noon 6 Consultants

Noon to 4 PM 8 Consultants

4 PM to 8 PM 12 Consultants

8 PM to Midnight 6 Consultants

Full time consultants are paid $14 per hour and they work any of the following 8 consecutive hour shifts:

8 AM to 4 PM

Noon to 8 PM

4 PM to Midnight

Part time consultants are paid $12 per hour and they work four-hour shifts.

At all times, there must be at least 2 full time consultants for each part time consultant on duty. Determine how many full time and part time consultants to employ during each work period to produce the lowest possible cost.

#### Solution Summary

Subject: Linear Programming

Details: The programs that can be used are Excel Slover, Data analyis, spread sheets, linear Programming and PERT/CPM models.

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19. A company that makes garments is unionized. Each full time employee works 40 hours per week,earns $13 per hour, and the union contract says that the number of full time employees can never drop below 20. Nonunion part time employees can be hired, but there must be at least 2 full time employees for each part time employee, and part time employees can work no more than 20 hours per week. They make $10 per hour. The company has 5,000 square feet of material available each week. The cost of this material is reflected in the Gross Profit per garment (but the cost of labor is not included in that cost). Fabrication requirements are as follow:

Product Material Required Labor Required Gross Profit per garment

A 2 square feet 30 minutes $8

B 1.5 square feet 45 minutes $10

C 1 square feet 40 minutes $6

Maximize the company's net profit: gross profit minus the cost of labor.

20. A Computer Center must have the following minimum number of consultants on duty during each 4-hour period:

8 AM to Noon 6 Consultants

Noon to 4 PM 8 Consultants

4 PM to 8 PM 12 Consultants

8 PM to Midnight 6 Consultants

Full time consultants are paid $14 per hour and they work any of the following 8 consecutive hour shifts:

8 AM to 4 PM

Noon to 8 PM

4 PM to Midnight

Part time consultants are paid $12 per hour and they work four-hour shifts.

At all times, there must be at least 2 full time consultants for each part time consultant on duty. Determine how many full time and part time consultants to employ during each work period to produce the lowest possible cost.