Explanation of Solution
Formulating a balanced transportation problem:
A balanced transportation problem is one in which the supply is equal to the total demand.
In the given problem, the variables are as follows:
- Let the supply from plant 1 (number of units) to customer 1 be represented as p11, to customer 2 be p12, to customer 3 be p13 and to customer 4 be p14.
- Let the supply from plant 2 to customer 1 be p21, to customer 2 be p22, to customer 3 be p23, to customer 4 be p24.
- Let the supply from plant 3 to customer 1 be p31, to customer 2 be p32, to customer 3 be p33, to customer 4 be p34.
The objective is to maximize profit. Total profit can be represented by the below mentioned linear
This is our objective function and we have to maximize it to gain maximum profit.
The constraints can be represented as follows:
In this customer 1 and 2 are using
Trending nowThis is a popular solution!
Chapter 7 Solutions
Operations Research : Applications and Algorithms
- A company owns the same asset in a ASIAN plant and in a UK plant . It has B $2,000,000 and a salvage value of 20% of B . For tax depreciation purposes, ASIA allows a straight line write-off over 5 years, while the UK allows SL write-off over 8 years. The general managers of the two plants want to know the difference in the depreciation amount for year 5.arrow_forwardIKEO is a furniture manufacturer which produces two sizes of wood blocks (type A and B) thatare used to make either a table or a chair. A table is made of a type A and a type B wood blocks,while a chair is made of a type A and two type B wood blocks (See Figure 1) A table makes RM 3 profit, and a chair makes RM 5 profit. If M number of type A and Nnumber of type B wood blocks are produced, how many tables and chairs should themanufacturer make to obtain the greatest profit?For example, let M = 12 and N = 12.By making 4 tables (4 type A and 4 type B) and 4 chairs (4 type A and 8 type B), themanufacturer gain profit as follows,Profit = (RM 3) × 4 + (RM 5) × 4 = RM 32.If the manufacturer makes 2 more tables and 1 less chair, the profit will be increased as follows,Profit = (RM 3) × 6 + (RM 5) × 3 = RM 33.Is this the greatest profit? Write a complete C++ program to help the manufacturer determine the greatest profit obtainfrom making tables and chairs with a given number of M type A and N…arrow_forwardAt Lummins Engine Corporation, production employeeswork 10 hours per day, four days per week. Each day ofthe week, at least the following number of employees mustbe working: Monday through Friday, seven employees; Saturday and Sunday, three employees. Lummins has set the following goals, listed in order of priority:■ Goal 1: Meet employee requirements with11 workers.■ Goal 2: The average number of weekend days offper employee should be at least 1.5 days.■ Goal 3: The average number of consecutive daysoff an employee gets during the week should notexceed 2.8 days.Use goal programming to determine how to schedule Lummins employees.arrow_forward
- Assuming all Ghanaians who are at least 18 years can choose between going to school or learning a trade. GHC 100 is invested every month for a person who chooses to go to school by the government till the person attains age 30 years provided he/she completes university. If he/she does not complete university, the payment is stopped at the time he/she exited. If the person chooses to learn a trade, the government pays GHC 2000 as apprentice fee to the madam or master who will take the person as an apprentice, and invest GHC 70 a month till age 30 years. If the person does not complete the apprenticeship, the payment is stopped at the time he/she exited. Remember that persons who are less than 18 years or 30 years and above do NOT qualify to enroll on this program. You are to write a c++ program for the above scenario. Your program should a) request a person’s name, age, what he/she wants to do (go to school or learn a trade), time of exit if any and disqualify the person if…arrow_forwardAssuming all Ghanaians who are at least 18 years can choose between going to school or learning a trade. GHC 100 is invested every month for a person who chooses to go to school by the government till the person attains age 30 years provided he/she completes university. If he/she does not complete university, the payment is stopped at the time he/she exited. If the person chooses to learn a trade, the government pays GHC 2000 as apprentice fee to the madam or master who will take the person as an apprentice, and invest GHC 70 a month till age 30 years. If the person does not complete the apprenticeship, the payment is stopped at the time he/she exited. Remember that persons who are less than 18 years or above 30 years do NOT qualify to enroll on this program.You are to write a java program for the above scenario. Your program should a) request a person’s name, age, what he/she wants to do (go to school or learn a trade), time of exit if any and disqualify the person if he/she does not…arrow_forwardAssuming all Ghanaians who are at least 18 years can choose between going to school or learning a trade. GHC 100 is invested every month for a person who chooses to go to school by the government till the person attains age 30 years provided he/she completes university. If he/she does not complete university, the payment is stopped at the time he/she exited. If the person chooses to learn a trade, the government pays GHC 2000 as apprentice fee to the madam or master who will take the person as an apprentice, and invest GHC 70 a month till age 30 years. If the person does not complete the apprenticeship, the payment is stopped at the time he/she exited. Remember that persons who are less than 18 years or 30 years and above do NOT qualify to enroll on this program. You are to write a c++ program for the above scenario. Your program should a) compute the total investment made for the person if he/she either finishes or exited along the way. b) display the results.arrow_forward
- Steelco manufactures two types of steel at three different steel mills. During a given month, each steel mill has 200 hours of blast furnace time available. Because of differences in the furnaces at each mill, the time and cost to produce a ton of steel differs for each mill. The time and cost for each mill are shown in the table below. Each month, Steelco must manufacture at least 500 tons of steel 1 and 600 tons of steel 2. Formulate an LP to minimize the cost of manufacturing the desired steel.arrow_forwardHOMEPRO is a furniture manufacturer which produces two sizes of wood blocks (type A and B) thatare used to make either a table or a chair. A table is made of a type A and a type B wood blocks,while a chair is made of a type A and two type B wood blocks (See Figure 1) A table makes RM 3 profit, and a chair makes RM 5 profit. If M number of type A and Nnumber of type B wood blocks are produced, how many tables and chairs should themanufacturer make to obtain the greatest profit?For example, let M = 12 and N = 12.By making 4 tables (4 type A and 4 type B) and 4 chairs (4 type A and 8 type B), themanufacturer gain profit as follows,Profit = (RM 3) × 4 + (RM 5) × 4 = RM 32.If the manufacturer makes 2 more tables and 1 less chair, the profit will be increased as follows,Profit = (RM 3) × 6 + (RM 5) × 3 = RM 33.Is this the greatest profit? Write a complete C++ program to help the manufacturer determine the greatest profit obtainfrom making tables and chairs with a given number of M type A and…arrow_forwardABC Company produces three electrical products—blenders, choppers, and toasters. The manufacturer has a maximum daily production budget of RM2000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 blenders, 300 choppers, and 150 toasters. The unit profit for blender is RM8, choppers, RM10, and toaster, RM7. The company desires to know the optimal product mix that will maximize profit. These products have the following resource requirements as shown in Table 1. Based on the report, answer the following questions and justify all your answers. Formulate the LP model for the above case study. Optimize the Company ABC production using linear programming simplex method. Suppose that the company would like to increase the profit of the toasters to RM9 per unit without affecting the optimum number of products to be produced based on earlier conditions. Based on the Sensitivity Report, advise the company if this can be accomplished and justify your answer. If this…arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole