Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Expert Solution & Answer
Chapter 4, Problem 12RP
Explanation of Solution
Optimal solution:
- Given table:
Product | Labor | Lumber | Paint | Price ($) | Variable Cost ($) |
1 | 1.5 | 2 | 3 | 26 | 10 |
2 | 3 | 3 | 2 | 28 | 6 |
3 | 2 | 4 | 2 | 31 | 7 |
- Let,
- x1 = Number of product I produced
- x2 = Number of product II produced
- x3 = Number of product III produced
- x4 = Amount of additional labor purchased
- x5 = Amount of additional paint purchased
- x6 = Amount of additional lumber purchased
- x7 = Amount of labor, lumber, and paint required for producing product I
- x8 = Amount of labor, lumber, and paint required for producing product II
- x9 = Amount of labor, lumber, and paint required for producing product III
- (d1)- = Underachievement in obtaining a profit of at least $10500
- (d1)+ = Overachievement in obtaining a profit of at least $10500
- (d2)- = Underachievement in purchasing no additional labor
- (d2)+ = Overachievement in purchasing no additional labor
- (d3)- = Underachievement in purchasing no additional paint
- (d3)+ = Overachievement in purchasing no additional paint
- (d4)- =Underachievement in purchasing no additional lumber
- (d4)+ = Overachievement in purchasing no additional lumber
...
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The WIX Company Civil Engineers consists of two divisions. The divisions are Water and Waste Water. The company sells engineering services to various customers. The following are the bill rates for the various staff classifications:
Vice President $200/hour
Senior Engineer $180/hour
Staff Engineer $150/hour.
The two divisions expect to bill the following hours:
Water- 10000 hours, vice president at 10% of the time, 30% of Senior Engineer time and remaining to Staff Engineers.
Waste Water- 6000 hours, vice president at 20% of the time, 20% of Senior Engineer time and remaining to Staff Engineers.
The Direct Labor costs per hours are as follows:
Vice President $80/hour
Senior Engineer $60/hour
Staff Engineer $40/hour.
The utilization for each staff members are as follows:
Vice President 60%
Senior Engineer 80%
Staff Engineer 90%.
The company has the following other costs:
Admin Salaries $90,000
Rent $100,000
Utilities $6,000
Benefits $76,000
Assume 20% of time for each staff member…
Kevin bought a new moulding machine for $3,000. The machine deteriorates with age and
requires to trade in for a new one every fifth year of usage. The resale value and the running
cost are given in below table.
Age of machine (year)
1
3
4
5
Maintenance cost ($)
600
700
800
900
1,000
Resale value ($)
2,000
1,333
1,000
750
500
A company manufactures three products 1, 2, and 3. Each product requires production time in three
departments as shown below:
PRODUCT DEPARTMENT 1 DEPARTMENT 2 DEPARTMENT 3
1
3 hr/unit
2 hr/unit
1 hr/unit
2
4 hr/unit
1 hr/unit
3 hr/unit
3
2 hr/unit
2 hr/unit
3 hr/unit
There are 500, 400, and 300 hours of production time available in the three departments, respectively. If
products 1, 2, and 3 contribute $3, $4, and $2.5 per unit to profit, answer the following questions:
(You may attach your solution or write in the box)
a)
Define the decision variables (2 marks).
b)
Write all constraints (3 marks).
c)
Write the objective function (define whether it is a maximization or minimization) (1.5 marks)
Chapter 4 Solutions
Introduction to mathematical programming
Ch. 4.1 - Prob. 1PCh. 4.1 - Prob. 2PCh. 4.1 - Prob. 3PCh. 4.4 - Prob. 1PCh. 4.4 - Prob. 2PCh. 4.4 - Prob. 3PCh. 4.4 - Prob. 4PCh. 4.4 - Prob. 5PCh. 4.4 - Prob. 6PCh. 4.4 - Prob. 7P
Ch. 4.5 - Prob. 1PCh. 4.5 - Prob. 2PCh. 4.5 - Prob. 3PCh. 4.5 - Prob. 4PCh. 4.5 - Prob. 5PCh. 4.5 - Prob. 6PCh. 4.5 - Prob. 7PCh. 4.6 - Prob. 1PCh. 4.6 - Prob. 2PCh. 4.6 - Prob. 3PCh. 4.6 - Prob. 4PCh. 4.7 - Prob. 1PCh. 4.7 - Prob. 2PCh. 4.7 - Prob. 3PCh. 4.7 - Prob. 4PCh. 4.7 - Prob. 5PCh. 4.7 - Prob. 6PCh. 4.7 - Prob. 7PCh. 4.7 - Prob. 8PCh. 4.7 - Prob. 9PCh. 4.8 - Prob. 1PCh. 4.8 - Prob. 2PCh. 4.8 - Prob. 3PCh. 4.8 - Prob. 4PCh. 4.8 - Prob. 5PCh. 4.8 - Prob. 6PCh. 4.10 - Prob. 1PCh. 4.10 - Prob. 2PCh. 4.10 - Prob. 3PCh. 4.10 - Prob. 4PCh. 4.10 - Prob. 5PCh. 4.11 - Prob. 1PCh. 4.11 - Prob. 2PCh. 4.11 - Prob. 3PCh. 4.11 - Prob. 4PCh. 4.11 - Prob. 5PCh. 4.11 - Prob. 6PCh. 4.12 - Prob. 1PCh. 4.12 - Prob. 2PCh. 4.12 - Prob. 3PCh. 4.12 - Prob. 4PCh. 4.12 - Prob. 5PCh. 4.12 - Prob. 6PCh. 4.13 - Prob. 2PCh. 4.14 - Prob. 1PCh. 4.14 - Prob. 2PCh. 4.14 - Prob. 3PCh. 4.14 - Prob. 4PCh. 4.14 - Prob. 5PCh. 4.14 - Prob. 6PCh. 4.14 - Prob. 7PCh. 4.16 - Prob. 1PCh. 4.16 - Prob. 2PCh. 4.16 - Prob. 3PCh. 4.16 - Prob. 5PCh. 4.16 - Prob. 7PCh. 4.16 - Prob. 8PCh. 4.16 - Prob. 9PCh. 4.16 - Prob. 10PCh. 4.16 - Prob. 11PCh. 4.16 - Prob. 12PCh. 4.16 - Prob. 13PCh. 4.16 - Prob. 14PCh. 4.17 - Prob. 1PCh. 4.17 - Prob. 2PCh. 4.17 - Prob. 3PCh. 4.17 - Prob. 4PCh. 4.17 - Prob. 5PCh. 4.17 - Prob. 7PCh. 4.17 - Prob. 8PCh. 4 - Prob. 1RPCh. 4 - Prob. 2RPCh. 4 - Prob. 3RPCh. 4 - Prob. 4RPCh. 4 - Prob. 5RPCh. 4 - Prob. 6RPCh. 4 - Prob. 7RPCh. 4 - Prob. 8RPCh. 4 - Prob. 9RPCh. 4 - Prob. 10RPCh. 4 - Prob. 12RPCh. 4 - Prob. 13RPCh. 4 - Prob. 14RPCh. 4 - Prob. 16RPCh. 4 - Prob. 17RPCh. 4 - Prob. 18RPCh. 4 - Prob. 19RPCh. 4 - Prob. 20RPCh. 4 - Prob. 21RPCh. 4 - Prob. 22RPCh. 4 - Prob. 23RPCh. 4 - Prob. 24RPCh. 4 - Prob. 26RPCh. 4 - Prob. 27RPCh. 4 - Prob. 28RP
Knowledge Booster
Similar questions
- Duyong Beach Resort is a contemporary hotel that offers rooms with private balconies that face the sea. Your company has obtained a contract from Duyong Beach Resort to design, maintain and update their online reservation system. All room's prices are subjected to tax and service charge. Therefore, total room price must include 6% of tax and 10% of service charge. Table 1 lists price per night, tax, and service charge for all type of rooms. (b) Room Type Standard (S) Deluxe (D) Family (F) (c) (a) float calculate_basicPrice (char roomType, int night) ● You have been assigned to create and implement this task using C program. You have been instructed to include the following functions: Table 1: List of Price for All Rooms Price per Night Tax Charge RM 230.00 RM 300.00 RM 420.00 accept roomType and reservation duration (night) from main function calculates basic room price for number of night(s) entered according to Table 1 return basic room price to main function void calculate_charges…arrow_forwardNizwa AC Maintenance company has been providing Air conditioners maintenance and service for their customers in Nizwa. Currentiy, they are handling Split AC, Window AC and charging the service charge according to the following table. | Air Conditoner Type Service Charge Split AC Window AC 15 Rials |20 Rials The total service cost is calculated based on the service charge of the AC and spare parts costs based on the formula show below: Total service cost = service charge + spare parts costs Write a Python program named acservice.py that should take two inputs: the air conditioner type and spare parts costs for 5 customers and store them in two different lists. The program has to calculate the total service cost for each customer and store them in a list. Finally, your program has to display the total service cost for 5 customers and maximum service cost. Run and test your program. Once done, submit the file named acservice.py at the link below.…arrow_forwardA real estate agency pays a sales representative monthly minimum income of 1000, 54 TL, additional allowance according to his/her title, plus 200 TL for each property sold by the sales representative in that month and a certain amount of the sales amount. Additional allowance amounts by title and bonus rates are given in the tables below: Title Additional Allowance (TL) Trainee (1) 250 Beginner (2) 350 Expert (3) Senior (4) 500 750 Sales Amount (TL) Bonus Rate (%) 0- 499.999,99 0.25 500.000- 999.999,99 0.5 1.000.000- 1.999.999,99 0.75 2.000.000-.. 1 By adhering the rules stated above, find the total salary amount of a sales representative for a particular month, by obtaining the title of a sales representative from the user (1 for the trainee, 2 for the novice, 3 for the specialist, 4 for the senior), the number of real estate sold this month and the total sales amount made by the sales representative. Write a C code that prints the total salary on the screen using the switch-case…arrow_forward
- Sprocket manufacturing. The manager of this production firm is faced with a potential problem: shortages in the supply of a vital gear sprocket. He is considering the development of an in-house capability to make the sprockets, knowing that the firm needs 35,000 such sprockets each year. If the firm elects to make the sprockets internally, then it must select one of the three possible production processes. Each has different costs, as shown in Table 10.17. Adopting a manual process may lead to union problems. The manager estimates the probability of these problems as 25%, and knows that if they do occur, then the variable cost will increase by $0.50 per sprocket. Further, if the semi-automatic or fully automatic option is selected, then additional training of personnel will be required. The amount and therefore the cost of training are uncertain. For the semi-automatic process, the fixed cost of basic training will add $15,000. However, there is a 20% chance the workers will need extra…arrow_forwardGENERATE THE DECISION VARIABLE SOLUTION AND GENERATE AN ANSWER REPORT 2. During the winter WeeMow Lawn Service contracts with customers for cutting lawns starting in the spring. WeeMow provides service to residential and commercial customers. The service has identified 50 possible residential customers and 15 potential commercial customers it has contacted. WeeMow services a customer once every 2 weeks during the growing season. A residential lawn on average takes 1.2 hours to cut, and a commercial property requires 5 hours to cut; the service's available work time is 8 hours, 6 days per week. The profit for a residential lawn is $23, and the profit for a commercial property is $61. The service has established a weekly budget of $350 for management, gas, and other materials, plus equipment repair. A residential lawn averages $12 in management, gas, material, and repair costs, and a commercial property averages $20 in costs. WeeMow wants to know how many residential and commercial jobs…arrow_forwardA real estate agency pays a sales representative monthly minimum income of 1000, 54 TL, additional allowance according to his/her title, plus 200 TL for each property sold by the sales representative in that month and a certain amount of the sales amount. Additional allowance amounts by title and bonus rates are given in the tables below: Title Additional Allowance (TL) Trainee (1) Beginner (2) 250 350 Expert (3) 500 Senior (4) 750 Sales Amount (TL) Bonus Rate (%) 0- 499.999,99 0.25 500.000- 999.999,99 0.5 1.000.000- 1.999.999,99 0.75 2.000.000-... 1 By adhering the rules stated above, find the total salary amount of a sales representative for a particular month, by obtaining the title of a sales representative from the user (1 for the trainee, 2 for the novice, 3 for the specialist, 4 for the senior), the number of real estate sold this month and the total sales amount made by the sales representative. Write a MATLAB code that prints the total salary on the screen using the…arrow_forward
- QUESTION 15 Al Watan supermarket has hire-purchases scheme for locals and expats. The customers will get the credit facility if they satisfy any of the following conditions: 1. The customer must hold the present job for more than 5 years and reside in the same place at least for 3 years. In this case, the customer will get credit upto rupees 300 omr. 2. The monthly salary of the customer must exceed 1000 omr and must hold the present job for more than 5 years. In this case credit will be given upto rupees 500 omr. 3. The monthly salary must exceed 1000 omr and reside at the same place at least for 3 years. In this case credit will be given upto 500 omr. 4. In the case, the customer's monthly salary exceeds 1000 omr, holds the present job for more than 5 years and also reside in the same place at least for the 3 years, the credit facility will be upto 1000 omr 5. The credit facility is rejected for all other customers. Prepare a Decision Table for this hire- purchase scheme. Attach File…arrow_forwardQUESTION 15 Al Watan supermarket has hire-purchases scheme for locals and expats. The customers will get the credit facility if they satisfy any of the following conditions: 1. The customer must hold the present job for more than 5 years and reside in the same place at least for 3 years. In this case, the customer will get credit upto rupees 300 omr. 2. The monthly salary of the customer must exceed 1000 omr and must hold the present job for more than 5 years. In this case credit will be given upto rupees 500 omr. 3. The monthly salary must exceed 1000 omr and reside at the same place at least for 3 years. In this case credit will be given upto 500 omr. 4. In the case, the customer's monthly salary exceeds 1000 omr, holds the present job for more than 5 years and also reside in the same place at least for the 3 years, the credit facility will be upto 1000 omr 5. The credit facility is rejected for all other customers. Prepare a Decision Table for this hire- purchase scheme.arrow_forwardAmarillo Video Store is planning a promotional give-away for its long-standing customers. If the customer has been a member for 18 months or more he/she will receive a coupon booklet allowing him/her to hire 4 movies for free. If during that same 18 months he/she has hired at least 12 videos, he/she will receive an additional 3 free movie hire vouchers. If the customer’s membership is less than 18 months and he/she has hired at least 12 videos then he/she will receive 2 free movie hire vouchers. All members will receive a Thank You letter and “Yentia Obiaa” music video. Construct a Decision Tree for the above scenario.arrow_forward
- Compute the volumes of cut and fill between stations 88+30 to 88+68 using the slope stake notes in the table on the following page. Use the average end area equation except for when the section produces a pyramid. In those situations, use the equation for a pyramid. Assume: Base Widths: cut = 50 ft; fill = 40 ft | Side Slopes: 2:1 | Gradient: -2% SURFACE GRADE STA L CL R ELEV. (ft) ELEV. (ft) C18.1 C10.2 92+00 891.6 874.63 C17.0 61.2 45.4 0 0 0 0 91+52 8575.6 875.59 0.0 25 20 20 25 F6.9 F11.4 91+00 864.5 876.63 F12.1 33.8 42.8 F8.2 F10.1 90+50 867.3 877.63 F10.3 36.4 40.2 F12.8 90+05 875.3 878.53 F3.2 20 45.6 C16.3 F12.2 89+73 879.2 879.17 57.6 44.4 C17.4 F8.3 89+59 885.6 879.45 C6.1 59.8 14 36.6 C10.2 F7.3 89+43 879.8 879.77 45.4 34.6 F16.1 89+08 873.7 880.47 F6.8 20 52.2 C16.8 F12.9 88+68 881.3 881.27 58.6 45.8 C24.0 88+30 890.9 882.03 C8.9 73.0 25arrow_forwardDraw decision table for Bookstores that get trade discount of a. 15% for orders from libraries and individuals b. 5%% extra allowed on orders of 6-19 copies per book titles c. 10% extra on orders of 20 -49 copies per book title d. 15% extra on orders of 50 or more copies per book title.arrow_forward1.Grass sod costs 35.00 per square meter and fencing costs 100.00 a linear foot. Display the total cost if the homeowner wants to sod and to fence his rectangular lot.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole