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Explanation of Solution
Determining the number of acres of corn and wheat to plant:
Let
Weekly revenue is calculated as follows:
The object function obtained from the above calculation is
Considering the constraints,
Constraint 1: Seven acres of land is available.
Constraint 2: 40 hours of labor are available each week.
Constraint 3: At least 30 bushels of corn must be produced
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Chapter 3 Solutions
Operations Research : Applications and Algorithms
- A certain grade of steel is graded according to the following condition: 1. Hardness must be greater than 40 2. Carbon contents must be less than 0.8 3. Tensile strength must be greater than 5000 The grades are as follows: § Grade is 10 if all the three conditions are met. § Grade is 9 if conditions 1 and 2 are met. § Grade is 8 if conditions 2 and 3 are met. § Grade is 7 if conditions 1 and 3 are met. § Grade is 6 if only one condition is met. § Grade is 5 if none of the conditions are met. Write a C++ program which will require user to give values of hardness, carbon content and tensile strength of the steel under consideration then determine the grade of steel and outputs the grade of the steelarrow_forwardWorkers at a particular company are paid at a rate of 150.00 per hour for up to 40 hours of work at hour over that is paid at a rate of 1.5 times the normal rate. From the worker’s gross pay, 14% is withheld for income tax, 5% withheld for social security system tax, and 13% is withheld for state income tax. An additional 10% is withheld if the worker has 3 or more covered dependents to cover extra cost of health insurance. Draw the flowchart and code the C program that outputs the worker’s gross pay, each withholding and the net take home pay for the week.arrow_forwardWorkers at a particular company are paid at a rate of 150.00 per hour for up to 40 hours of work at hour over that is paid at a rate of 1.5 times the normal rate. From the worker’s gross pay, 14% is withheld for income tax, 5% withheld for social security system tax, and 13% is withheld for state income tax. An additional 10% is withheld if the worker has 3 or more covered dependents to cover extra cost of health insurance. Draw the flowchart and write or code the C program that outputs the worker’s gross pay, each withholding and the net take home pay for the week.arrow_forward
- Harry and Melissa Jacobson produce handcrafted furniture in a workshop on their farm. They have obtained a load of 600 board feet of birch froma neighbor and are planning to produce round kitchen tables and ladder-back chairs during the next 3 months. Each table will require 30 hours oflabor, each chair will require 18 hours, and between them they have a total of 480 hours of labor available. A table requires 40 board feet of woodto make, and a chair requires 15 board feet. A table earns the couple $575 in profit, and a chair earns $120 in profit. Most people who buy a tablealso want four chairs to go with it, so for every table that is produced, at least four chairs must also be made, although additional chairs can also besold separately. Formulate and solve an integer programming model to determine the number of tables and chairs the Jacobsons should make tomaximize profit. What is the maximized profit?arrow_forwardDuring the tax season, every Friday, the J & J tax accounting firm provides assistance to people who prepare their own tax returns. Their charges are as follows:a. If a person has low income (<= 25,000) and the Consulting time is less than or equal to 30 minutes, there are no charges; otherwise the service charges are 40% of the regular hourly rate for the time over 30 minutes.b. For others, if the Consulting time is less than or equal to 20 minutes, there are no service charges; otherwise, service charges are 70% of the regular hourly rate for the time over 20 minutes.(For example, suppose that a person who has low income is spent 1 hour and 15 minutes, and the hourly rate is $70.00. Then the billing amount is $70.00 x 40 x (45/60) = $21.00). Write a program that prompts the user to enter the hourly rate, the total Consulting time, and whether the person has a low income. The program should output the building of Mount your program must contain a function that takes as input…arrow_forwardhe Dash Cell Phone Company charges customers a basic rate of $5 per month to send text messages. Additional rates are as follows: The first 100 messages per month, regardless of message length, are included in the basic bill. An additional three cents are charged for each text message after the 100th message, up to and including 300 messages. An additional two cents are charged for each text message after the 300th message. Federal, state, and local taxes add a total of 14 percent to each bill. Design a flowchart or pseudocode for the following: c. A program that continuously accepts data about text messages until a sentinel value is entered, and displays details only about customers who send more than 100 text messages.arrow_forward
- he Dash Cell Phone Company charges customers a basic rate of $5 per month to send text messages. Additional rates are as follows: The first 100 messages per month, regardless of message length, are included in the basic bill. An additional three cents are charged for each text message after the 100th message, up to and including 300 messages. An additional two cents are charged for each text message after the 300th message. Federal, state, and local taxes add a total of 14 percent to each bill. Design a flowchart or pseudocode for the following: d. A program that continuously accepts data about text messages until a sentinel value is entered, and displays details only about customers whose total bill with taxes is over $10.arrow_forwardq no 3: A certain grade of steel is graded according to the following condition: Hardness must be greater than 40 Carbon contents must be less than 0.8 Tensile strength must be greater than 5000 The grades are as follows: Grade is 10 if all the three conditions are met. Grade is 9 if conditions 1 and 2 are met. Grade is 8 if conditions 2 and 3 are met. Grade is 7 if conditions 1 and 3 are met. Grade is 6 if only one condition is met. Grade is 5 if none of the conditions are met. Write a C++ program which will require user to give values of hardness, carbon content and tensile strength of the steel under consideration then determine the grade of steel and outputs the grade of the steel.arrow_forwardA farmer is planning to raise wheat and barley. Each acre of wheat yields a profit of $50, and each acre of barley yields a profit of $70. To sow the crop, two machines, a tractor and a tiller are rented. The tractor is available for 150 hours, and the tiller is available for 200 hours. Sowing an acre of wheat requires 4 hours of tractor time and 1 hour of tilling. Sowing an acre of barley requires 3 hours of tractor time and 2 hours of tilling. How many acres of each crop should be planted to maximize the farmer’s profit? (Let W be the number of acres of wheat to be planted, B the number of acres of barley to be planted and P the profit) What is the objective function for the problem? Excluding the non-negative constraint, how many constraints does the problem have? What is the linear programming model of the problem? In the initial tableau, what is the leaving variable? What is the pivot element in the initial tableau? What is the optimal solution to the problem? After how many…arrow_forward
- Shamira Laundry has designed a new calculation system for their shop. The price for each type is as follows: 10 Туре Price Clothes RM 15 for 1 kilogram blankets / towels RM 6 for 1 kilogram RM 10 for 1 kilogram comforter Only one type can be washed at a time. This laundry shop also provides discounts to its customers as follow: Total price >= RM30 Discount 10% from total price >= RM20 dan = RM15 danarrow_forwardThe Livewright Medical Supplies Company has a total of 12 salespeople it wants to assign to three regionsthe South, the East, and the Midwest. A salesperson in the South earns $600 in profit per month for the company, a salesperson in the East eams $540, and a salesperson in the Midwest earns $375. The southern region can have a maximum assignment of 5 salespeople. The.company has a total of $750 per day available for expenses for all 12 salespeople. A salesperson in the South has average expenses of $80 per day, a salesperson in the East has average expenses of$70_pér day, and a salesperson in the Midwest has average daily expenses of $50. The company wants to detemine the number of salespeople to assign to each region to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer.arrow_forwardThe Livewright Medical Supplies Company has a total of 12 salespeople it wants to assign to three regions-the South, the East, and the Midwest. A salesperson in the South earns $600 in profit per month for the company, a salesperson in the East earns $540, and a salesperson in the Midwest earns $375. The southern region can have a maximum assignment of five sales- people. The company has a total of $750 per day available for expenses for all 12 salespeople. A salesperson in the South has average expenses of $80 per day, a salesperson in the East has average expenses of $70 per day, and a salesperson in the Midwest has average daily expenses of $50. The company wants to determine the number of salespeople to assign to each region to maximize profit. a. Formulate an integer programming model for this problem. b. Solve this model by using the computer.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole