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: Cut Profit 4 10 1,3 2,2 3,1 1,1,2 1,2,1 2,1,1 1,1,1,1 (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 algorithm using OUBuild script following the above steps.

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: Cut Profit 4 10 1,3 2,2 3,1 1,1,2 1,2,1 2,1,1 1,1,1,1 (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 algorithm using OUBuild script following the above steps.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter11: Nonlinear Programming

Section11.1: Review Of Differential Calculus

Problem 6P

See similar textbooks

Similar questions

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 = 12
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:
In the rod cutting problem, we are given a rod of length n, along with pi, which indicates the price of a rod/piece of length pi, for i = 0, 1, 2, ..,n. Consider the following instance: po = 0, pı = 2, p2 = 7, p3 = 15, p4 = 16 and n = 4. Let r; denote the maximum profit you can obtain by cutting a rod of length i into smaller pieces (or by making no cuts). What is the respective value of ro, rı,., r4? You must show how you obtained the values by applying the recurrence.
A ticket from Indianapolis to Orlando on DeleastAirlines sells for $150. The plane can hold 100 people. Itcosts $8,000 to fly an empty plane. The airline incurs variablecosts of $30 (food and fuel) for each person on the plane.If the flight is overbooked, anyone who cannot get a seatreceives $300 in compensation. On the average, 95% of allpeople who have a reservation show up for the flight. Tomaximize expected profit, how many reservations for theflight should be taken by Deleast? (Hint: The @Riskfunction RISKBINOMIAL can be used to simulate thenumber of passengers who show up. If the number ofreservations taken is in cell A2, then the formulaRISKBINOMIAL(A2,.95)will generate the number of customers who actually showup for a flight!)
We are given three ropes with lengths n₁, n2, and n3. Our goal is to find the smallest value k such that we can fully cover the three ropes with smaller ropes of lengths 1,2,3,...,k (one rope from each length). For example, as the figure below shows, when n₁ = 5, n₂ 7, and n3 = 9, it is possible to cover all three ropes with smaller ropes of lengths 1, 2, 3, 4, 5, 6, that is, the output should be k = 6. = Devise a dynamic-programming solution that receives the three values of n₁, n2, and n3 and outputs k. It suffices to show Steps 1 and 2 in the DP paradigm in your solution. In Step 1, you must specify the subproblems, and how the value of the optimal solutions for smaller subproblems can be used to describe those of large subproblems. In Step 2, you must write down a recursive formula for the minimum number of operations to reconfigure. Hint: You may assume the value of k is guessed as kg, and solve the decision problem that asks whether ropes of lengths n₁, n2, n3 can be covered by…
Exercise 4 20= 10+4+6 The rod-cutting problem consists of a rod of n units long that can be cut into integer-length pieces. The sale price of a piece i units long is Pi for i = 1,...,n. We want to apply dynamic programming to find the maximum total sale price of the rod. Let F(k) be the maximum price for a given rod of length k. 1. Give the recurrence on F(k) and its initial condition(s). 2. What are the time and space efficiencies of your algorithm? Now, consider the following instance of the rod-cutting problem: a rod of length n=5, and the following sale prices P1=2, P2=3, P3-7, P4=2 and P5=5.
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.
IKEO 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.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 type B wood…
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?
A ski rental agency has n pairs of skis, where the height of the the ith pair of skis is si . There are n skiers who wish to rent skis, where the height of the ith skier is hi. Ideally, each skier should obtain a pair of skis whose height matches her/his own height as closely as possible. We would like to assign skis to skiers so that the sum of the absolute differences of the heights of each skier and her/his skis is minimized. Design a greedy algorithm for the problem. Prove the correctness of your algorithm. (Hint: Start with two skis and two skiers. How would you match them? Continue to three skis and three skiers, and identify a strategy.)
There are n trading posts along a river numbered 1, 2, 3, ..., n. At any of the posts you can rent a canoe to be returned at any other post downstream. (It is impossible to paddle against the river, since it is too fast..) For each possible departure point i and each possible arrival point j (> i), the cost of a rental from i to j is known: it is C[i,j] > 0. However, it can happen that the cost of renting from i to j is higher than the total costs of a series of shorter rentals from i to j. In this case you can return the first canoe at some post k between i and j and continue your journey in a second (and, maybe, third, fourth ...) canoe. There is no extra charge for changing canoes in this way. Give a O(n2) time dynamic programming algorithm to determine the minimum cost of a trip from trading post 1 to trading post n.
There are four possible ways to cross the river for a person. Let the first location is denoted by L1, second one is by L2, third one is by L3, and fourth one is by L4 arranged from north to south. A tiger can wait at one of the specified 4 locations. If the location chosen is same by both person and the tiger, then the payoff to the tiger is 1. If both person and tiger chosen adjacent locations the payoff to the tiger is 0.5. If both chosen location are distinct and non – adjacent then the payoffs were 0. In the present scenario, what is the value of the game to the tiger?