Question: a) Consider the continuous knapsack problem (CKP) with the following formulation: xmaxs.t.j=1nwjxjj=1npjxjd,0xj1,j[n]. In fact, CKP is the LP relaxation of 1dj=dwjUj. Explain in words why

a) Consider the continuous knapsack problem (CKP)

a) Consider the continuous knapsack problem (CKP) with the following formulation: xmaxs.t.j=1nwjxjj=1npjxjd,0xj1,j[n]. In fact, CKP is the LP relaxation of 1dj=dwjUj. Explain in words why an optimal solution x to (CKP) can be found by sorting the indices in [n] such that p1w1p2w2pnwn, determining the key index j with k=1j1pkdjj[n]. a) Consider the continuous knapsack problem (CKP) with the following formulation: xmaxs.t.j=1nwjxjj=1npjxjd,0xj1,j[n]. In fact, CKP is the LP relaxation of 1dj=dwjUj. Explain in words why an optimal solution x to (CKP) can be found by sorting the indices in [n] such that p1w1p2w2pnwn, determining the key index j with k=1j1pkdjj[n]

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related General Management Questions!

TACKLE ALL PARTSP5 Problem 1 The Airfare Problem1. You are trying to get the cheapest airfare that you can. You just called up and found that the ticket home will cost $400, and it cannot be refunded...

Planning Demand and Supply in a Supply Chain Capacity Planning and Assignment 1 utdallas.edu/~metin Outline Capacity Planning Product-to-plant Assignment utdallas.edu/~metin 2 Deterministic Capacity...

/* knapsack.h * implements simple knapsack data structure as a linked list * NOTE: a function may update the value of input argument *knapsack if it changes the first node of the knapsack to another...

/* knapsack.h * implements simple knapsack data structure as a linked list */ /* pointer to linked list node data structure */ typedef struct listitem* listitemptr; /* data structure to use as linked...

3. Given n items {1,.., n), and each item i has a nonnegative weight wi and a distinct value v. We can carry a maximum weight of W in a knapsack. The items are blocks of cheeses so that for each item...

Question 1 [10 marks]: Consider the instance of continuous knapsack problem with the knapsack capacity 150 and the item information as follows: Item Weight Value 1 70 $420 2 30 $120 3 40 $400 4 50...

please show all work 7. Continuous vs. Discrete Knapsack Problem Given values v[1 ... 6] = (5,5,9, 4, 4, 12), weights w[1 ... 6) = (1,4,3,4, 1,6) and capacity W = 9. a. Suppose these data constitute...

[Knapsack Covers] Consider the binary knapsack problem max x + 2x2 + x3 + 7x4 s.t. 100xi + 70x2 +50x3 + 60x4 150 Since not all variables in the cover S can be in the knapsack simultaneously, we can...

Question 4 . Consider the following 0 - 1 knapsack problem: m a m i z e 1 2 x 1 + 1 1 x 2 + 8 x 3 + 6 x 4 subject t o 8 x 1 + 8 x 2 + 6 x 3 + 5 x 4 2 0 x 1 , x 2 , x 3 , x 4 i n { 0 , 1 } ( a ) Solve...

The mixed knapsack problem. In class, we talked about the knapsack problems. There were two "pure" versions of the knapsack problem, the fractional knapsack problem (dealing with items that are...

A hockey puck with a weight of 0.50 lb is sliding freely across a section of very smooth (frictionless) horizontal ice. (a) When it is sliding freely, how does the upward force of the ice on the puck...

Mr. Davis owns one of the largest jam, jelly and preserves plants in the country. He's based in Massachusetts, just outside of Boston. Davis prides himself on producing the finest products in the...

Aultlple Choice Question tockholders' equity can be defined by which one of these formulas? Stockholders' equity = Assets / Liabilities Stockholders' equity = Assets Stockholders' equity = Assets -...

When older adults have difficulty with transportation and communication, or may be reluctant to request needed assistance to which they are entitled, they may be in need of: Group of answer choices...