Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
expand_more
expand_more
format_list_bulleted
Concept explainers
Expert Solution & Answer
Chapter 3.6, Problem 2P
Explanation of Solution
Calculation to obtained the maximizes the NPV from the given investment:
The Net Present Value (NPV) of an investment is the amount by which the investment will increase the firm’s value.
Assuming the annual rate interest, “r = 0.10”, the user can compute the NPV for investment 1 as,
Now, the user computes the NPV for investment 1 as,
Therefore, the NPV of investment 1 is larger than investment 2.
Let, “x1” be the fraction of investment 1 that is undertaken and “x2” be the fraction of investment 2 that is undertaken.
The objective function is to maximize the NPV of the investment.
Therefore, maximize
Constraint 1:
At time 0, $10000 is available for investment
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
QUESTION 9
What is one advantage of AABB over Bounding Spheres?
Computing the optimal AABB for a set of points is easy to program and
can be run in linear time. Computing the optimal bounding sphere is a
much more difficult problem.
The volume of AABB can be an integer, while the volume of a Bounding
Sphere is always irrational.
An AABB can surround a Bounding Sphere, while a Bounding Sphere
cannot surround an AABB.
To draw a Bounding Ball you need calculus knowledge.
Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution.
A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows:
- Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.$0.30 per gram.- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.0.90 per gram.
The dietary needs of the specialty food require a minimum of 30% protein and a maximum of 5% fiber. The farm wishes to determine the optimum ratios of corn and soybeans to produce a feed with minimal costs while maintaining nutritional constraints and ensuring that a minimum of 800 grams of feed is used daily.
Restrictions
1. The total amount of feed should be at least 800 grams per day.2. The feed should contain at least 30% protein…
Suppose that there are four items available which can be put into a knapsack that has a capacity of 14 pounds. The weights of the items are 5,7,4, and 3 pounds respectively. Their utilities are 8,11,6 and 4 respectively. Find the optimal solution that maximizes the total utility of the knapsack.
Chapter 3 Solutions
Operations Research : Applications and Algorithms
Ch. 3.1 - Prob. 1PCh. 3.1 - Prob. 2PCh. 3.1 - Prob. 3PCh. 3.1 - Prob. 4PCh. 3.1 - Prob. 5PCh. 3.2 - Prob. 1PCh. 3.2 - Prob. 2PCh. 3.2 - Prob. 3PCh. 3.2 - Prob. 4PCh. 3.2 - Prob. 5P
Ch. 3.2 - Prob. 6PCh. 3.3 - Prob. 1PCh. 3.3 - Prob. 2PCh. 3.3 - Prob. 3PCh. 3.3 - Prob. 4PCh. 3.3 - Prob. 5PCh. 3.3 - Prob. 6PCh. 3.3 - Prob. 7PCh. 3.3 - Prob. 8PCh. 3.3 - Prob. 9PCh. 3.3 - Prob. 10PCh. 3.4 - Prob. 1PCh. 3.4 - Prob. 2PCh. 3.4 - Prob. 3PCh. 3.4 - Prob. 4PCh. 3.5 - Prob. 1PCh. 3.5 - Prob. 2PCh. 3.5 - Prob. 3PCh. 3.5 - Prob. 4PCh. 3.5 - Prob. 5PCh. 3.5 - Prob. 6PCh. 3.5 - Prob. 7PCh. 3.6 - Prob. 1PCh. 3.6 - Prob. 2PCh. 3.6 - Prob. 3PCh. 3.6 - Prob. 4PCh. 3.6 - Prob. 5PCh. 3.7 - Prob. 1PCh. 3.8 - Prob. 1PCh. 3.8 - Prob. 2PCh. 3.8 - Prob. 3PCh. 3.8 - Prob. 4PCh. 3.8 - Prob. 5PCh. 3.8 - Prob. 6PCh. 3.8 - Prob. 7PCh. 3.8 - Prob. 8PCh. 3.8 - Prob. 9PCh. 3.8 - Prob. 10PCh. 3.8 - Prob. 11PCh. 3.8 - Prob. 12PCh. 3.8 - Prob. 13PCh. 3.8 - Prob. 14PCh. 3.9 - Prob. 1PCh. 3.9 - Prob. 2PCh. 3.9 - Prob. 3PCh. 3.9 - Prob. 4PCh. 3.9 - Prob. 5PCh. 3.9 - Prob. 6PCh. 3.9 - Prob. 7PCh. 3.9 - Prob. 8PCh. 3.9 - Prob. 9PCh. 3.9 - Prob. 10PCh. 3.9 - Prob. 11PCh. 3.9 - Prob. 12PCh. 3.9 - Prob. 13PCh. 3.9 - Prob. 14PCh. 3.10 - Prob. 1PCh. 3.10 - Prob. 2PCh. 3.10 - Prob. 3PCh. 3.10 - Prob. 4PCh. 3.10 - Prob. 5PCh. 3.10 - Prob. 6PCh. 3.10 - Prob. 7PCh. 3.10 - Prob. 8PCh. 3.10 - Prob. 9PCh. 3.11 - Prob. 1PCh. 3.11 - Show that Finco’s objective function may also be...Ch. 3.11 - Prob. 3PCh. 3.11 - Prob. 4PCh. 3.11 - Prob. 7PCh. 3.11 - Prob. 8PCh. 3.11 - Prob. 9PCh. 3.12 - Prob. 2PCh. 3.12 - Prob. 3PCh. 3.12 - Prob. 4PCh. 3 - Prob. 1RPCh. 3 - Prob. 2RPCh. 3 - Prob. 3RPCh. 3 - Prob. 4RPCh. 3 - Prob. 5RPCh. 3 - Prob. 6RPCh. 3 - Prob. 7RPCh. 3 - Prob. 8RPCh. 3 - Prob. 9RPCh. 3 - Prob. 10RPCh. 3 - Prob. 11RPCh. 3 - Prob. 12RPCh. 3 - Prob. 13RPCh. 3 - Prob. 14RPCh. 3 - Prob. 15RPCh. 3 - Prob. 16RPCh. 3 - Prob. 17RPCh. 3 - Prob. 18RPCh. 3 - Prob. 19RPCh. 3 - Prob. 20RPCh. 3 - Prob. 21RPCh. 3 - Prob. 22RPCh. 3 - Prob. 23RPCh. 3 - Prob. 24RPCh. 3 - Prob. 25RPCh. 3 - Prob. 26RPCh. 3 - Prob. 27RPCh. 3 - Prob. 28RPCh. 3 - Prob. 29RPCh. 3 - Prob. 30RPCh. 3 - Graphically find all solutions to the following...Ch. 3 - Prob. 32RPCh. 3 - Prob. 33RPCh. 3 - Prob. 34RPCh. 3 - Prob. 35RPCh. 3 - Prob. 36RPCh. 3 - Prob. 37RPCh. 3 - Prob. 38RPCh. 3 - Prob. 39RPCh. 3 - Prob. 40RPCh. 3 - Prob. 41RPCh. 3 - Prob. 42RPCh. 3 - Prob. 43RPCh. 3 - Prob. 44RPCh. 3 - Prob. 45RPCh. 3 - Prob. 46RPCh. 3 - Prob. 47RPCh. 3 - Prob. 48RPCh. 3 - Prob. 49RPCh. 3 - Prob. 50RPCh. 3 - Prob. 51RPCh. 3 - Prob. 52RPCh. 3 - Prob. 53RPCh. 3 - Prob. 54RPCh. 3 - Prob. 56RPCh. 3 - Prob. 57RPCh. 3 - Prob. 58RPCh. 3 - Prob. 59RPCh. 3 - Prob. 60RPCh. 3 - Prob. 61RPCh. 3 - Prob. 62RPCh. 3 - Prob. 63RP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Similar questions
- 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_forward1. Consider an instance of the Knapsack Problem without repetitions with 4 items, having weights and values as follows. The weights (in pounds) are w1=2, w2 =7, w3 =10, w4 =12. The dollar values of these items are respectively v1 = 12, v2 = 28, v3 = 30, v4 = 5. The capacity of the knapsack is 12. (a) Find the optimal solution for Fractional Knapsack. (b) Find the optimal solution for 0-1 Knapsack.arrow_forwardSolve the following problem and find the optimal solution.arrow_forward
- A given Knapsack with maximal Weight capacity is 8Kg. There are some items can be chosen and taken into Knapsack. Each item has own weight and profit shown as follows. Please find the maximal profit of Knapsack after some items are selected and put into this Knapsack and its maximal Weight capacity isn't exceeded. item ID Weight 4Kg 5Kg 2Kg 1kg 6Kg A B с D E Profit 4500 5700 2250 1100 8700 The maximal profit of this Knapsack to taken some items and total weight is no exceeded the weight capacity : The last item is taken and put into this Knapsack is: The second item is taken and put into this Knapsack is : The first item is taken and put into this Knapsack is:arrow_forwardA circus is planning a tower act in which individuals stand on top of one another's shoulders. Each individual must be both shorter and lighter than the person below him or her for practical and aesthetic reasons. Write a way to determine the maximum feasible number of people in such a tower given the heights and weights of each individual in the circus.arrow_forwardA person is cutting a long board of wood into different length of pieces. Each cutting has fixed width 2 cm lengths. Given that each cutting with different length has a different price, Now, we are required to help this person to find the optimal cuts in order to increase his income. Consider following example showing different cut's lengths and their equivalent prices. Input: board length = 4 Length [] = [1, 2, 3, 4, 5, 6, 7, 8] Price [ 1= [2, 6, 8, 10, 14, 17, 19, 20] Output: Best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12 [Explanation: the possible cuts and profit of each is as follows: Cut Profit 4 1,3 2,2 3,1 1,1,2 1,2,1 2,1,1 1,1,1,1 10 (2+8) = 10 (6+6) = 12 (8+2) = 10 (2+2+6) = 10 (2+6+2) = 10 (6+2+2) = 10 (2+2+2+2) = 8 As noted the best cut is two pieces of length 2 each to gain revenue of 6+ 6 = 12 To answer question 1, you need to do the following: 1. Write an algorithm to find the optimal cuts in order to increase the person income's 2. Implement the…arrow_forward
- A person is cutting a long board of wood into different length of pieces . Each cutting has fixed width 2 cm lengths. Given that each cutting with different length has a different price, Now, we are required to help this person to find the optimal cuts in order to increase his income. Consider following example showing different cut’s lengths and their equivalent prices. Input: board length = 4 Length [ ] = [1, 2, 3, 4, 5, 6, 7, 8] Price [ ] = [2, 6, 8, 10, 14, 17, 19, 20] Output: Best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12 [Explanation: the possible cuts and profit of each is as follows: As noted the best cut is two pieces of length 2 each to gain revenue of 6 + 6 = 12arrow_forwardIf it is possible to create an optimal solution for a problem by constructing optimal solutions for its subproblems, then the problem possesses the corresponding property. a) Subproblems which overlap b) Optimal substructure c) Memorization d) Greedyarrow_forwardThe shaded region in the given figure above illustrates an unbounded feasible region. Which of the following is true? I. The maximum value for the objective function does not exist in an unbounded feasible region. II. If the objective function is Min Z=x+y, then it's maximum is 25 at (25,0). III. If the objective function is Max Z=-x+2y, then it's minimum is O at (25,0). IV. Unbounded feasible regions have either maximum or minimum value. 024 10 (25 0) -20 -10 10 O A. I O B. II O C.I and II O D. II and IVarrow_forward
- Please explain! Dynamic Programming can be used to solve numerous real-life optimization problems. Consider these six problems.Five of these six problems have elegant and efficient solutions using Dynamic Programming, but one of these problems does not. Which of these six problems cannot be solved using Dynamic Programming? Choice 1 of 6: Given a rod, and a set of prices p[i] for each cut of length i, determine how to cut the rods to maximize your profit Choice 2 of 6: Given a rod, and a set of prices p[i] for each cut of length i, determine how to cut the rods to minimize your profit Choice 3 of 6: Given a graph, determine the shortest path from the start vertex to the end vertex without repeating any edges Choice 4 of 6: Given a graph, determine the longest path from the start vertex to the end vertex without repeating any edges Choice 5 of 6: Given a sequence of integers, determine the longest increasing subsequence of that sequence Choice 6 of 6: Given a sequence of integers,…arrow_forwardThe drug Taxoprol costs $60 per unit to produce. Currently the exchange rate is 0.667 $/euro (don't worry about today's actual exchange rate, use the value given in this problem) and we are charging 150 euros per unit for Taxoprol. Current demand for Taxoprol is 100 units, and it is estimated that the elasticity for Taxoprol is 2.5. Assuming a linear demand curve, determine the price (in euros) for Taxoprol if the exchange rate moves to 0.8 $/euro. We want to maximize profits in US dollars. Create a nonlinear programming model and use the Solver add-in with GRG Nonlinear.arrow_forwardMaximum weight = 20The above problem is a 0/1 Knapsack problem. Here there are 7 different objects labelled from A to G. The objective of this problem is to carry the different objects in your bag in such a way such that the profit is maximized. But you have to make sure that your bag does not exceed the maximum weight i.e. the maximum weight that this bag can carry is less than or equal to 15. Remember you can carry an object exactly once. Now it is your job to use Genetic Algorithm to solve this problem. 1. Encode the problem and create an initial population of 4 different chromosomes 2. Think of an appropriate fitness function to this problem and give proper justification. 3. Use the fitness function to calculate the fitness level of all the chromosomes in your population 4. Perform natural selection and select the two fittest chromosomes 5. Use the parents from (4) and perform crossover to get 2 offspring 6. Perform mutation and check the fitness of the final offspring. Comment…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