Concept explainers
Explanation of Solution
Given data:
The farmer Jane owns 45 acres of land and planning to plant with wheat or corn.
On planting wheat, she yields $200 profit and corn yields $300 profit.
Given table:
Wheat | Corn | |
Labor | 3 workers | 2 workers |
Fertilizer | 2 tons | 4 tons |
Consider
Objective function:
Considering the constraints,
Constraint 1: Total acres of land used
Constraint 2: Maximum number of workers to be used is 100
Constraint 3: Maximum tons of fertilizers are 120 tons.
Expressing the constraint 1 in terms of
Expressing the constraint 2 in terms of
Expressing the constraint 3 in terms of
Therefore, the mathematical model of given LP is,
Subject to the constraints,
Converting the inequality constraint without adding any variable:
The coordinate points for the constraint
If
If
The coordinate points for the constraint
If
If
The coordinate points for the constraint
If
If
Therefore, the coordinate point for the constraint
Graph:
From the above graph, it is known that the vertices of the feasible region lies in the points
Calculating the value of the objective function to find the end points:
Therefore, the value of
Substituting the value of
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Introduction to mathematical programming
- Refer to the following hypothetical situation to come up with a linear programming solution maximizing profit for a local ice-cream shop. The objective: On average, you get $1 in revenue from every pound of ice cream you sell. You get $5 for every ice cream cake (neglect the cake size here) you sell in the market. You need to bring in as much revenue as you can to keep your shop running on a day-to-day basis. The decisions: You need to figure out what mix of ice creams (per pound) and the number of ice cream cakes to produce each month to maximize total profit. The constraints: It costs $0.5 or 50 cents to produce a pound of ice cream and $4 to produce one ice cream cake (on average). You have a budget of $100 per day to devote to producing new products for sale. You must also store this stuff in your 10 cubic meter freezer. Every pound of ice cream takes up .1 cubic meters once packed, and every cake (on average) takes up 0.25 cubic meters. You can’t store these products elsewhere…arrow_forwardSuppose, you are working in a company ‘X’ where your job is to calculate the profit based on their investment. If the company invests 100,000 USD or less, their profit will be based on 75,000 USD as first 25,000 USD goes to set up the business in the first place. For the first 100,000 USD, the profit margin is low: 4.5%. Therefore, for every 100 dollar they spend, they get a profit of 4.5 dollar. For an investment greater than 100,000 USD, for the first 100,000 USD (actually on 75,000 USD as 25,000 is the setup cost), the profit margin is 4.5% where for the rest, it goes up to 8%. For example, if they invest 250,000 USD, they will get an 8% profit for the 150,000 USD. In addition, from the rest 100,000 USD, 25,000 is the setup cost and there will be a 4.5% profit on the rest 75,000. Investment will always be greater or equal to 25,000 and multiple of 100. Complete the RECURSIVE methods below that take an array of integers (investments) and an iterator (always sets to…arrow_forwardSuppose, you are working in a company ‘X’ where your job is to calculate the profit based on their investment. If the company invests 100,000 USD or less, their profit will be based on 75,000 USD as first 25,000 USD goes to set up the business in the first place. For the first 100,000 USD, the profit margin is low: 4.5%. Therefore, for every 100 dollar they spend, they get a profit of 4.5 dollar. For an investment greater than 100,000 USD, for the first 100,000 USD (actually on 75,000 USD as 25,000 is the setup cost), the profit margin is 4.5% whereas for the rest, it goes up to 8%. For example, if they invest 250,000 USD, they will get an 8% profit for the 150,000 USD. In addition, from the rest 100,000 USD, 25,000 is the setup cost and there will be a 4.5% profit on the rest 75,000. The investment will always be greater or equal to 25,000 and multiple of 100. Complete the RECURSIVE methods below that take an array of integers (investments) and an iterator (always sets to…arrow_forward
- A construction company has four large bulldozers located at four different garages. The bulldozers are to be moved to four different construction sites. The distances in miles between the bulldozers and the construction sites are given below. Bulldozer/ A B C D Site Students 1 90 75 75 80 solve it 2 35 85 55 65 yourself 3 125 95 90 105 4 45 110 95 115 How should the bulldozers be moved to the construction sites in order to minimize the total distance traveled?arrow_forwardA farmer in Georgia has a 100-acre farm on which to plant watermelons and cantaloupes. Every acre planted with watermelons requires 50 gallons of water per day and must be prepared for planting with 20 pounds of fertilizer. Every acre planted with cantaloupes requires 75 gallons of water per day and must be prepared for planting with 15 pounds of fertilizer. The farmer estimates that it will take 2 hours of labor to harvest each acre planted with watermelons and 2.5 hours to harvest each acre planted with cantaloupes. He believes that watermelons will sell for about $3 each, and cantaloupes will sell for about $1 each. Every acre planted with watermelons is expected to yield 90 salable units. Every acre planted with cantaloupes is expected to yield 300 salable units. The farmer can pump about 6,000 gallons of water per day for irrigation purposes from a shallow well. He can buy as much fertilizer as he needs at a cost of $10 per 50-pound bag. Finally, the farmer can hire laborers to…arrow_forwardSuppose, you are working in a company ‘X’ where your job is to calculate the profit based on their investment.If the company invests 100,000 USD or less, their profit will be based on 75,000 USD as first 25,000 USD goes to set up the business in the first place. For the first 100,000 USD, the profit margin is low: 4.5%. Therefore, for every 100 dollar they spend, they get a profitof 4.5 dollar.For an investment greater than 100,000 USD, for the first 100,000 USD (actually on 75,000 USD as 25,000 is the setup cost), the profit margin is 4.5% where for the rest, it goes up to 8%. For example, if they invest 250,000 USD, they will get an 8% profit for the 150,000 USD. In addition, from the rest 100,000 USD, 25,000 is the setup cost and there will be a 4.5% profit on the rest 75,000. Investment will always be greater or equal to 25,000 and multiple of 100.Complete the RECURSIVE methods below that take an array of integers (investments)and an iterator (always sets to ZERO(‘0’) when the…arrow_forward
- The 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_forwardThere is a 15 days tour of visiting 5 national parks. There is a stay of two day at each park. So, 2 multiplied by 5 = 10 days are spent at staying in those 5 parks. Now the remaining days left are 15 - 10 = 5 days which have to be spent on travelling on visiting these parks. Mode of travel will be : Travel by car from SF to YO = $ 130 which is one way cost. It will take half day in travelling from SF to YO. Travel by air from YO to YE = $ 400 . It will take half day in travelling. Now, the total days left for travelling is 4 days. Travel by car from YE to GT = $ 70 . It will take whole one day in travelling. Travel by car from GT to MR will take two days and will cost $ 100 . Travel from MR to back to SF = $ 450 by air. It will take half day for this air travel. This is the best economical travel incurring traveeling cost of $ 1150 . Table 1. Need code in python using PULP and linear programming librariesarrow_forwardEneros Inc. is buying a new machine for $450,000. The life of the machine is 10 years, and a bank is ready to finance the entire amount at a rate of 10% per year. The bank would like Eneros to pay back interest due on the loan, and the loan amount broken into 10 equal payment of $45,000 per year. i.e. Pay interest due at end of each year PLUS $45,000 principle payment per year.a. Please create the scenario in excel.arrow_forward
- Bianca is preparing special dishes for her daughter’s birthday. It takes her a minutes to prepare the first dish, and each following dish takes b minutes longer than the previous dish. She has t minutes to prepare the dishes. For example, if the first dish takes a = 10 minutes and b = 5, then the second dish will take 15 minutes, the third dish will take 20 minutes, and so on. If she has 80 minutes to prepare the dishes, then she can prepare four dishes because 10 + 15 + 20 + 25 = 70. Write a program that prompts the user to enter the values of a, b, and t, and outputs the number of dishes Bianca can prepare.arrow_forwardThe Mayfree Appliance Company requires sheet metal for its appliances. The company can purchase long coils of sheet metal in two different widths: 65 inches and 40 inches. The company must purchase the coils by linear foot of length: $1.20 per foot for a 64-inch coil and $1.00 per foot for a 40-inch coil. (This implies that a square foot, say, of the wider coil is less expensive.) Up to 4000 feet of the 65-inch coil is available, and up to 6000 feet of the 40-inch coil is available. There are manufacturing requirements for six different widths: 50, 45, 40, 35, 20, and 10 inches. Mayfree’s requirements are expressed as lengths of the various widths. The company requires 1000 feet of 50-inch width, 2500 feet of 45-inch width, 3000 feet of 40-inch width, 2300 feet of 35-inch width, 1300 feet of 20-inch width, and 2000 feet of 10-inch width. Determine how much of each width coil Mayfree should purchase and how it should cut the coils into various widths to meet its requirements at minimal…arrow_forwardA school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 7 sophomores, 9 juniors, and 7 seniors are eligible to be on the committee, in how many ways can the committee be chosen? Your answer is:arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole