A medical clinic performs three types of medical tests that use the same machines. Tests A, B, and C take 15 minutes, 30 minutes, and 1 hour, respectively, with respective profits of $120, $240, and $500. The clinic has four machines and four workers available. One person is qualified to do test A, two to do test B, and one to do test C. If the clinic has a rush of customers for these tests, how many of each type should it schedule in a 10-hour day to maximize its profit?

A medical clinic performs three types of medical tests that use the same machines. Tests A, B, and C take 15 minutes, 30 minutes, and 1 hour, respectively, with respective profits of $120, $240, and $500. The clinic has four machines and four workers available. One person is qualified to do test A, two to do test B, and one to do test C. If the clinic has a rush of customers for these tests, how many of each type should it schedule in a 10-hour day to maximize its profit?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 64P

See similar textbooks

Similar questions

Solve the question below using the attached excel templates with formulas for renting both slow and fast copies (labeled in the excel tabs). Question: The Decision Sciences Department is trying to determine whether to rent a slow or a fast copier. The department believes that an employee’s time is worth $15 per hour. The slow copier rents for $4 per hour, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15 per hour, and it takes an employee an average of six minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour?
A public hospital employs volunteers to attend the reception between 8:00 A.M. and 10:00 P.M. Each volunteer works three consecutive hours, except those who enter at 8:00 P.M., who only work 2 hours. An approximation to the minimum need for volunteers is through a staggered function in two-hour intervals, which start at 8:00 A.M. and they are 4, 6, 8, 6, 4, 6 and 8 volunteers per interval. As most of the volunteers are pensioners, they are willing to offer their services at any time of the day (8:00 A.M. to 10:00 P.M.). However, as most charities compete for your services, the amount required should be kept as low as possible. Determine an optimal schedule of start time and number of volunteers.
Dalton Desk makes two different types children's desks: a regular model (R) and a deluxe model (D) with an extra shelf for book storage. Both types of desks go through Daltons' three production departments: fabrication, assembly, and packing/shipping, but required a different number of minutes in each department. For example, the regular desk needs 60 minutes of fabrication time, 45 minutes of assembly, and 15 minutes in packing & shipping. The deluxe model needs 120 minutes of fabrication time, 60 minutes in assembly, and 20 minutes in packing & shipping. Dalton has 850 hours of production time available in fabricating department, 450 hours available in its assembly department, and 200 hours available in its packaging and shipping department. Dalton reports unit profits of $6 and $8 for its regular and deluxe desks, respectively. What is the objective function? What is the fabrication constraint? What is the assembly constraint?What is the Shipping and Packing constraint?
A catering company must have the following number of clean napkins available at the beginning of each of the next four days: day 1: 15, day 2: 12, day 3: 18, and day 4: 6. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs $0.10 per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs $0.06 per napkin, and a napkin cleaned via slow service is available two days after they were last used. New napkins can be purchased for a cost of $0.20 per napkin. Part A: Formulate the problem as a minimum cost transportation problem.
A catering company must have the following number of clean napkins available at the beginning of each of the next four days: day 1: 15, day 2: 12, day 3: 18, and day 4: 6. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs $0.10 per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs $0.06 per napkin, and a napkin cleaned via slow service is available two days after they were last used. New napkins can be purchased for a cost of $0.20 per napkin. Part A: Formulate the problem as a minimum cost transportation problem. Part B: Solve the problem (provide exact values for all variables and the optimal objective function).
A call center employs 1,425 agents. Every month 57 employees leave the company and 57 new employees are hired. a. How long on average does an agent work for this call center (in months) Suppose the cost of hiring and training a new agent is $1,140. The manager of this call center believes that increasing agents’ salaries would keep them working longer at the company. The manager wants to increase the average time that an agent works for the call center to 36 months, or three years. b-1. Given the current average working time for agents at this call center, determine the current annual cost for hiring and training. b-2. Assuming the average time that an agent works for the call center is increased to 36 months, determine the new annual cost for hiring and training. b-3. If the time an agent works for the call center is increased to 36 months on average, how much could the company save on hiring and training costs over a year?
You are working for Advance Technology, a company that produces three different devices for the military. The three devices that you produce are Main-bus Servo Modules, Secondary Trigger Activators, and Guidance Couplers. Advance Technology has two manufacturing facilities, the Croswell facility and the Grass Lake facility. Each day, the Croswell facility can produce 8 Main-bus Servo Modules, 4 Secondary Trigger Activators, and 4 Guidance Coupler at a cost of $1,800. Each day, the Grass Lake facility can produce 6 Main-bus Servo Modules, 12 Secondary Trigger Activators, and 2Guidance Couplers at a cost of $1,600. An order from the U.S. Navy for 210 Main-bus Servo Modules, 150 Secondary Trigger Activators, and 90 Guidance Couplers is received. Your boss has assigned to you the task of determining the number of days that each facility should operate to meet the order placed for the three devices at a minimum cost to your company.
A furniture company manufactures chairs and desks. The sawing department cuts the lumber for both products, which is then sent to separate assembly departments. Assembled items are sent to the painting department for finishing. The daily capacity of the sawing department is 200 chairs or 80 desks. The chair assembly department can produce 120 chairs daily, and the desk assembly department 60 desks daily. The paint department has a daily capacity of either 150 chairs or 100 desks. Given that the profit per chair is $50 and that of a desk is $100. Formulate the problem as a linear program to determine the optimal product mix for the company.
A car wash offers two different types of wash services, deluxe wash and standard wash. The deluxe wash require(s) three steps: pre-wash, wash and dry. The standard wash only require(s) two steps: wash and dry. The pre-wash step has a capacity of 7 cars per hour. The wash step has a capacity of 11 cars per hour. The dry step has a capacity of 10 cars per hour. The demand for deluxe wash is 7 cars per hour and the demand for standard wash is 11 cars per hour. Instruction: Round to the nearest integer percentage. What is the implied utilization of the bottleneck resource?
A company manufactures plastic bottles, buckets, and cups. The profit units are $10 for a plastic bottle, $25 for a bucket,and 58 for a bag of cups. The machine that makes the goods has a capacity of 400 hours each month. The bottle takestwo hours to make, the bucket three hours, and the cup one hour. The company has a total of 890 units of plastic. Plasticbottles require three units, buckets five units, and cups one unit. In addition, there are 200 kg of a novel chemicalcomponent. This unique chemical component is employed in plastic bottles (2 kilogram), buckets (4 kg), and cups (0.5kg) . There is an order to produce only 50 bags of plastic cup. The company wants to find the optimal plan to maximizeprofit. Use the Simplex method to solve this problem.
Rienzi Farms grows sugar cane and soybeans on its 500 acres of land. An acre of soybeans brings a $1000 contribution to overhead and profit; an acre of sugar cane has a contribution of $2500. Because of a government program no more than 150 acres may be planted in soybeans. During the planting season 1800 hours of planting time will be available. Each acre of soybeans requires 2 hours, while each acre of sugar cane requires 6 hours. The company seeks maximum contribution from its planting decision. a) Formulate the problem as a linear program. b) Solve using the corner-point method (graphical method).
A small shoe manufacturer makes two styles of shoes: oxfords and loafers. Two machines are used in the process: a cutting machine and a sewing machine. Each type of shoe requires 15 min per pair on the cutting machine. Oxfords require 10 min of sewing per pair, and loafers require 20 min of sewing per pair. Because the manufacturer can hire only one operator for each machine, each process is available for just 8 hours a day. Set up a system of linear inequalities that describes the number of pairs of each style of shoes that the manufacturer can produce within required working hours.