A janitorial service, Mother’s Helpers, provide workers to clean office buildings during late evening hours using workers with two skill levels, 1 and 2. Each level 1 person is paid $12 per hour and each level 2 person is paid $8 per hour. The workers wash floors and vacuum offices. Each level 1 person can vacuum 9 offices per hour, whereas level 2 person can vacuum only 2 offices per hour. Each level 1 person can wash 2 floors per hour; whereas level 2 person can wash 3 floors per hour. In order to complete a new job in the allotted time, 18 offices must be vacuumed per hour and 12 floors must be washed per hour. Use Excel and determine the number of each type of person that will be needed to complete the job within the allotted time and minimum cost and provide algebraic model

A janitorial service, Mother’s Helpers, provide workers to clean office buildings during late evening hours using workers with two skill levels, 1 and 2. Each level 1 person is paid $12 per hour and each level 2 person is paid $8 per hour. The workers wash floors and vacuum offices. Each level 1 person can vacuum 9 offices per hour, whereas level 2 person can vacuum only 2 offices per hour. Each level 1 person can wash 2 floors per hour; whereas level 2 person can wash 3 floors per hour. In order to complete a new job in the allotted time, 18 offices must be vacuumed per hour and 12 floors must be washed per hour. Use Excel and determine the number of each type of person that will be needed to complete the job within the allotted time and minimum cost and provide algebraic model

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 64P

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janitorial service, Mother’s Helpers, provide workers to clean office buildings during late evening hours using workers with two skill levels, 1 and 2. Each level 1 person is paid $12 per hour and each level 2 person is paid $8 per hour. The workers wash floors and vacuum offices. Each level 1 person can vacuum 9 offices per hour, whereas level 2 person can vacuum only 2 offices per hour. Each level 1 person can wash 2 floors per hour; whereas level 2 person can wash 3 floors per hour. In order to complete a new job in the allotted time, 18 offices must be vacuumed per hour and 12 floors must be washed per hour.
The Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) Minimize the under and…
The Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. a) Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) b) Minimize the under…
The Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal, and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. a) Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) b) Minimize the…
Tiny Toy Company makes three types of new toys: the tiny tank, the tiny truck, and the tiny turtle. Plastic used in one unit of each is 1.5, 2.0 and 1.0 pounds, respectively. Rubber for one unit of each toy is 0.5, 0.5, and 1.0 pounds, respectively. Also, each tank uses 0.3 pounds of metal, and the truck uses 0.6 pounds of metal during production. The average weekly availability for plastic is 16,000 pounds, 9,000 pounds of metal, and 5,000 pounds of rubber. It takes two hours of labor to make one tank, two hours for one truck, and one hour for a turtle. The company allows no more than 40 hours a week for production (priority #1). Finally, the cost of manufacturing one tank is $7, 1 truck is $5 and 1 turtle is $4; a target budget of $164,000 is initially used as a guideline for the company to follow. Minimize over-utilization of the weekly available supply of materials used in making the toys and place twice as much emphasis on the plastic (priority #2) I understand…
Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1 7 5 2 5 5 3 5 2 The shaper is available for 125 hours, and the grinder is available for 95 hours. No more than 170 units of component 3 can be sold, but up to 1050 units of each of the other components can be sold. In fact, the company already has orders for 625 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. If more time could be made available on the grinder, how much would it be worth? If required, round your answers to two decimal places.$ _____ per minute, since the dual value is _____ on the grinder at the optimal solution.
Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1 6 4 2 4 5 3 4 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 800 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. (a) Formulate and solve for the recommended production quantities. component 1 unitscomponent 2 unitscomponent 3 units (b) What are the objective coefficient ranges for the three components? (If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) component 1 blank to blank units…
A manufacturing process has 12 workers and 6 stations. The process iscompleted in the order given below. Where there are multiple workers within a station,each worker works independently on his/her own unit. Assume inventory buffers areallowed between each station.Station Staffing Processing time (hoursper unit per worker)A 2 2.20B 1 1.25C 3 2.00D 2 2.60E 3 3.00F 1 0.75What is the maximum number of units per hour that can be produced? Assume they startthe day with inventory at each station to work on
Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows: Machine Component Shaper Grinder 1 6 4 2 4 5 3 4 2 The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 900 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively. (a) Formulate and solve for the recommended production quantities. component 1 unitscomponent 2 unitscomponent 3 units (b) What are the objective coefficient ranges for the three components? (If there is no upper or lower limit, enter NO LIMIT. Round your answers to the nearest integer.) component 1 to unitscomponent 2 to…
The Northside Bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank, including adequate customer service, employee breaks, and so on. On Fridays, the bank is open from 9:00 A.M. to 7:00 P.M. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here. Time No. of Tellers Time No. of Tellers 9:00 a.m.-10:00 a.m. 6 2:00 p.m.-3:00 p.m. 7 10:00 a.m.-11:00 a.m. 5 3:00 p.m.-4:00 p.m. 6 11:00 a.m.-Noon 7 4:00 p.m.-5:00 p.m. 8 Noon-1:00 p.m. 11 5:00 p.m.-6:00 p.m. 7 1:00 p.m.-2:00 p.m. 9 6:00 p.m.-7:00 p.m. 5 Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost…
The Northside Bank is working to develop an efficient work schedule for full-time and part-time tellers. The schedule must provide for efficient operation of the bank, including adequate customer service, employee breaks, and so on. On Fridays, the bank is open from 9:00 A.M. to 7:00 P.M. The number of tellers necessary to provide adequate customer service during each hour of operation is summarized here. Time No. of Tellers Time No. of Tellers 9:00 a.m.-10:00 a.m. 6 2:00 p.m.-3:00 p.m. 8 10:00 a.m.-11:00 a.m. 4 3:00 p.m.-4:00 p.m. 6 11:00 a.m.-Noon 6 4:00 p.m.-5:00 p.m. 6 Noon-1:00 p.m. 10 5:00 p.m.-6:00 p.m. 7 1:00 p.m.-2:00 p.m. 11 6:00 p.m.-7:00 p.m. 4 Each full-time employee starts on the hour and works a 4-hour shift, followed by a 1-hour break and then a 3-hour shift. Part-time employees work one 4-hour shift beginning on the hour. Considering salary and fringe benefits, full-time employees cost the bank $15 per hour ($105 a day), and part-time employees cost…
nSilver Paints manufactures paints products. Their best selling colors in the outdoor paints category are Grey, Beige & Black. The capacity at the plant is 200 paint containers per week. nThe 3 best selling colors use the same basic raw materials but require different ratios of additives. nGrey requires 4 gallons of additive A and 2 gallon of additive B per container, nBeige requires 2 gallons of additive A and 2 gallons of additive B per container, nBlack requires 2 gallon of additive A and 1 gallons of additive B per container. nThe supply of both of these additives is quite limited. Each week, this product line is allocated only 550 gallons of additive A per week and 380 gallons of additive B. nThe profit margin of each product: Grey $75, Beige $73, Black $70 Question: How many of each of the 3 colors should be produced each week?