Explanation of Solution
Given:
Let
Let
Objective function:
Considering the constraints,
Constraint 1 and 2: At most, 4000 woods are available for purchase.
Constraint 3: At most, 6000 hours of labor are available to manufacture
Expressing the constraint 1 in terms of variables:
Expressing
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Chapter 3 Solutions
Operations Research : Applications and Algorithms
- 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_forwardAn electrical utility company charges the domestic customers with the rate provided below: 3. For the first 200 kWh (1 - 200 kWh) per month: For the next 100 kWh (201 – 300 kWh) per month: For the next 300 kWh (301 – 600 kWh) per month: For the next 300 kWh (601 – 900 kWh) per month: For the next kWh (901 kWh onwards) per month: 21.80 cents/kWh 33.40 cents/kWh 51.60 cents/kWh 54.60 cents/kWh 57.10 cents/kWh. Draw the flowchart to show the sequence of calculating the rate, starting from obtaining the monthly energy consumption until printing out the amount payable.arrow_forwardPakistan Railway has hired you for the task of repair of its rail networks of province SINDH, the cost of the repair of track between the different cities are presented in the given Table. For instance, the entry (KHI,HYD)= 10 in the table tells us the cost of building a rail connection between these two cities is 10 (in million rupees) You are required to develop a rail network that connects all the cities by at least one path with the smallest cost by avoiding multiple paths to the same city. Hence the problem becomes the finding of Minimum spanning tree in a graph. Your job is as follows; a) Translate the given information in the form of Graph (Vertices & edges) b) Use Greedy Algorithms (Kruskal’s , if the S5 is odd & Prim’s technique , if S5 is even) to build rail connections in this scenario. Apply this algorithm and show all steps up to the final routes. c) What is the cost of repairing of resulting rail network?arrow_forward
- %9 ۱/۱ العنوان قص نسخ لصق حذف قص Conduct stability analysis under extreme load condition for the design of a 50 m high concrete gravity dam. All Assume that the bi dam behaves as a monolithic structure. Normal operating level: 45 m Shear strength at foundation level: 5 MPa Compressive strength of concrete: 30 MPa Compressive strength of base material: 25 MPa Friction coefficient at foundation level: 0.75 Specific weight of concrete: 24 kN/m Specific gravity of water: 10 kN/m Level of sediment accumulated in the reservoir: 5 m Underwater specific gravity of the sediment accumulated in the reservoir: 11 kN/m (Q-32", K-(1-sinQy(1+sinQ)] Earthquake coefficients: k 0.1, k. 0.05 Ice force: 100 kN/m Tail water is not present. It is envisaged that the lifting pressure will be reduced by 40% with the drainage structures to be constructed. で 0.00 T el | Marrow_forwardA pharma company produces two types of Active Pharmaceutical Ingredients (API), API T and API C. Many biochemical materials are usually necessary to produce a small amount of APIs. To produce 1kg of API T, one must use 5kg and 10kg of biochemical materials W and P, respectively. To produce 1kg of API C, one must use 4 kg and 5 kg of biochemical materials W and P, respectively. It costs $100 and $60 to produce 1kg API T and C, respectively. The pharma company can spend $600 at most to produce the APIs. Taking into account yield uncertainties of the APIs, the pharma company has two goals as follows. Goal 1: The total amount of biochemical material W should be 35kg or more (i.e., approximately 35kg, ideally more than 35kg. In the worst case, the amount is less than 35kg.) Goal 2: The total amount of biochemical material P should be 60kg or less (i.e., approximately 60kg, ideally less than 60kg. In the worst case, the amount is more than 60kg.) The pharma company must determine how much…arrow_forwardi need the answer quicklyarrow_forward
- A large apple farm distributes their apples in boxes that they can source from any one of a number of nearby box manufacturers. Each box manufacturer makes only one box type that holds a specific number of apples - so a box from one manufacturer might hold 24 apples, while a box from another might hold 13. The apple farm can only choose one box supplier each year (a decision they make each year based on price), but they can then order an unlimited number of boxes of that type. The farm likes to be prepared, and creates large batches of apples to pack before the decision about which box type to use has been made. The farm also likes to limit waste, and tries to set the number of apples in these large batches such that they can fill an integer number of boxes perfectly with no apples left over. In creating these batches, although the farm doesn't yet know the exact capacity of the boxes they will buy, they know a list of possible values the box capacity will take. For example, if the…arrow_forwardA new Company plans to allocate some or all of its monthly advertising budget of GH¢82,000 in the Mankato area. It can purchase local radio spots at GH¢120 per spot, local TV spots at GH¢600 per spot, and local newspaper advertising at GH¢220 per insertion. The company's policy requirements specify that the company must spend at least GH¢40,000 on TV and allow monthly newspaper expenditures up to GH¢60,000. The payoff from each advertising medium is a function of the size of its audience. The general experience of the firm is that the values of insertions and spots in terms of "audience points" (arbitrary unit), are as given below: ----------------------------------------------------------------- Radio 40 audience points per spot TV 180 audience points per spot Newspapers 320 audience points per insertion -----------------------------------------------------------------…arrow_forwardTwo buses, X and Y, start their journey at the same time on a 950 km route. Bus X gives a 1-hour break after every 3 hours' drive. So, it is at rest at the 4th, 8th, 12th, 16th, 20th, ... hours. Bus Y gives a 1-hour break after every 4 hours' drive. So, it is at rest at the 5th, 10th, 15th, 20th, 25th,... hours. You are given the speeds of the two buses Vx and Vy as 80 and 75, respectively. Write a program that does the following: • Evaluate and display at the end of every hour the distance traveled by each bus. When either one of the buses reach their destination, the evaluations terminate. Depending on whether X or Y or both reach their destination in the last hour, display one of the following messages before stopping (where n is the number of hours): o "Within hour n, bus X reaches its destination." "Within hour n, bus Y reaches its destination." o "Within hour n, both buses reach their destinations." Sample screen output: After hour 1, X is at 80 km, Y is at 75 km. After hour 2, X…arrow_forward
- Ina de chopper, the average load current is 30 A, chopping frequency s 250 Hz. Supply voltage is 110 volts. Calculate the ON and OFF periods of the chopper if the load resistance is 202.arrow_forwardA regional telephone company had 5.2 million subscribers. Each of their telephones is connected to a central office by a copper twisted pair. The average length of these twisted pairs is 3.5 km. How much is the copper in the local loops worth? Assume that the cross section of each strand is a circle 1.2 mm in diameter, the density of copper is 8.4 grams/cm3, and that copper sells for $15.00 per kilogram.arrow_forwardTN Communications provides cellular telephone services. The company is planning to expand into the Cincinnati area and is trying to determine the best location for its transmission tower. The tower transmits over a radius of 10 miles. The locations that must be reached by this tower are shown in the following figure. x y Florence 10 24 Covington 12 16 Hyde Park 16 18 Evendale 12 22 I was able to get the answer to question a, which was: x y Tower Location 12 22 Max Distance 6 And I almost got the answer to question b, but I'm missing the y, what is the answer? x y Tower Location 12.51 Max Distance 4.45arrow_forward
- Operations Research : Applications and AlgorithmsComputer ScienceISBN:9780534380588Author:Wayne L. WinstonPublisher:Brooks Cole