/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q27E Show that the change-making prob... [FREE SOLUTION] | 91影视

91影视

Show that the change-making problem (Exercise) can be formulated as an integer linear program. Can we solve this program as an LP, in the certainty that the solution will turn out to be integral (as in the case of bipartite matching)? Either prove it or give a counterexample.

Short Answer

Expert verified

As little more than a result, it is a collection of non-negative integers represented asn1+n2+...+nn forn coins, as well as the number of coins must always be kept to a minimum.

Step by step solution

01

Consider the information

鈥 During linear regression, every problem is actually parameters are stated as linear relationships, as well as the greatest profit or minimal cost is calculated utilizing linear relationships.

鈥 It's a type of mathematical programming in which connections are optimised depending on limitations.

02

Numerical (Int) Linear Problem

鈥 Obtaining the value of can be used to solve the integer issue.ni as one if the nth If a coin is chosen, the goal is to go to zero.

o Minimizen1+n2+...+nn

o Subject tox1n1+x2n2+...+xnnn=v

鈥 As either a result, the linear connection may be expressed as follows:

o Minimizei=1nni

o Subject toi=1nxini=v

鈥 Exactly integer values are contained inside the combination of something like a number of coins with their value.

As a result, the issue may be expressed as such an integers linear problem.

Linear programming:

鈥淵es鈥. This linear programme could be used to fix the issues..

03

Conclusion

鈥 Given are the coins with denominations x1+x2+...+xnand the objective is to find the change for the value .

鈥 Linear programming can be used to solve the presented problem.

鈥 It necessitates the use of the fewest possible coins.

鈥 Suppose nidenotes the number of times the ithused n1+n2++nncoins.

鈥 Therefore, it is a set of non-negative integers forncoins written asand the number of coins must be minimized.

鈥 That minimization should indeed be done under the constraint that the total value of the coins chosen is the same as the supplied value.v.

鈥 Another criteria for such an optimization seems to be that the total of the coins chosen equals the provided value.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In a satisfiable system of linear inequalities

a11x1++a1nxnb1:am1x1++amnxnbm

we describe the inequality as forced-equal if it is satisfied with equality by every solution x = (x1,...,xn)of the system. Equivalently,Piajixibj is not forced-equal if there exists an x that satisfies the whole system and such that Piajixibj.

For example, in

x1+x22-x1-x2-2x11-x20

For the linear program

maxx12x3x1x212x2x31x1,x2,x30

Prove that the solution(x1,x2,x3)=(3/2,1/2,0) is optimal

Question: Duckwheat is produced in Kansas and Mexico and consumed in New York and California. Kansas produces 15 shnupells of duckwheat and Mexico 8. Meanwhile, New York consumes 10 shnupells and California 13. The transportation costs per shnupell are \(4 from Mexico to New York, \)1 from Mexico to California, \(2 from Kansas to New York, and \)3 and from Kansas to California. Write a linear program that decides the amounts of duckwheat (in shnupells and fractions of a shnupell) to be transported from each producer to each consumer, so as to minimize the overall transportation cost

Matching pennies. In this simple two-player game, the players (call them Rand C) each choose an outcome, heads or tails. If both outcomes are equal, Cgives a dollar to R; if the outcomes are different, Rgives a dollar to C.

(a) Represent the payoffs by a22 matrix.

(b) What is the value of this game, and what are the optimal strategies for the two players?

The Canine Products company offers two dog foods, Frisky Pup and Husky Hound, that are made from a blend of cereal and meat. A package of Frisky Pup requires 1 pound of cereal and 1.5pounds of meat, and sells for \(7. A package of Husky Hound uses 2 pounds of cereal and 1 pound of meat, and sells for \)6. Raw cereal costs\(1per pound and raw meat costs\)2per pound. It also costslocalid="1658981348093" \(1.40to package the Frisky Pup and localid="1658981352345" \)0.60to package the Husky Hound. A total of localid="1658981356694" 240,000pounds of cereal and pounds of meat are available each month. The only production bottleneck is that the factory can only package 110,000bags of Frisky Pup per month. Needless to say, management would like to maximize profit.

(a) Formulate the problem as a linear program in two variables.

(b) Graph the feasible region, give the coordinates of every vertex, and circle the vertex maximizing profit. What is the maximum profit possible?

See all solutions

Recommended explanations on Computer Science Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.