Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 24.4, Problem 1E
Program Plan Intro
To find the feasible solutions of edges by using suitable constraints of the graph.
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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…
Solution that
Consider the following linear programming model:
Max 2X1 + 3X2
Subject to:
X1 ≤ 2
X2 ≤ 3
X1 ≤ 1
X1, X2 ≥ 0
This linear programming model has:
a.
alternate optimal solutions
b.
infeasible solution
c.
redundant constraint
d.
unbounded solution
Chapter 24 Solutions
Introduction to Algorithms
Ch. 24.1 - Prob. 1ECh. 24.1 - Prob. 2ECh. 24.1 - Prob. 3ECh. 24.1 - Prob. 4ECh. 24.1 - Prob. 5ECh. 24.1 - Prob. 6ECh. 24.2 - Prob. 1ECh. 24.2 - Prob. 2ECh. 24.2 - Prob. 3ECh. 24.2 - Prob. 4E
Ch. 24.3 - Prob. 1ECh. 24.3 - Prob. 2ECh. 24.3 - Prob. 3ECh. 24.3 - Prob. 4ECh. 24.3 - Prob. 5ECh. 24.3 - Prob. 6ECh. 24.3 - Prob. 7ECh. 24.3 - Prob. 8ECh. 24.3 - Prob. 9ECh. 24.3 - Prob. 10ECh. 24.4 - Prob. 1ECh. 24.4 - Prob. 2ECh. 24.4 - Prob. 3ECh. 24.4 - Prob. 4ECh. 24.4 - Prob. 5ECh. 24.4 - Prob. 6ECh. 24.4 - Prob. 7ECh. 24.4 - Prob. 8ECh. 24.4 - Prob. 9ECh. 24.4 - Prob. 10ECh. 24.4 - Prob. 11ECh. 24.4 - Prob. 12ECh. 24.5 - Prob. 1ECh. 24.5 - Prob. 2ECh. 24.5 - Prob. 3ECh. 24.5 - Prob. 4ECh. 24.5 - Prob. 5ECh. 24.5 - Prob. 6ECh. 24.5 - Prob. 7ECh. 24.5 - Prob. 8ECh. 24 - Prob. 1PCh. 24 - Prob. 2PCh. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - Prob. 6P
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- DPP. Solve by backward recursive equation defining its stages in order to find the optimal solutionarrow_forwardConstruct a PYTHON program code for an inequality constraint minimization via logarithm barrier method.(OPTIMIZATION) For this problem minimize –x + /y subject to (x – 5)² + (y – 3)² < 3/2 x < 5 -arrow_forwardSolver is guaranteed to find the global minimum (if it exists) if the objective function is concave and the Constraints are linear. True or Falsearrow_forward
- Solve the following LPP by graphical Method Maximize Z =22X1+18X2 Subject to constraints: 960X1+640X2≤15 360X1+X2≤20 and X1,X2≥0 (Note the X1 And X2 are variables and not to be mistaken with muliplication symbol)arrow_forwardQuestion : Part A: Write the Linear Programming equations in standard equality form. Part B: Solve the original Linear programming equations graphically (to scale). Clearly identify the feasible region and, if one or more exist, the optimal solution(s) (provide exact values for x1, X2, and Z). Maximize the objective function Z = -4x1 + 2x2 Subject To constraints: -2x1 + 2x2 s7 X12 2 X1 - 4x2 s 0 2x1 + 2x2 2 10 X1, x2 2 0arrow_forwardThe following figure shows a linear programming problem where the shaded region represents the polytope of feasible solutions, the colored lines represent constraint functions, and the black lines represent the contours of the objective function. Darker lines of the objective function contour represent larger values. It also shows five different points, all of which lie within the polytope. The linear program attempts to find the maximum value. Which point corresponds to a solution of the linear program? 2 (B) 5 1 3 E 4 20 …..arrow_forward
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