To solve: The given linear programming problem.
Answer to Problem 29AYU
Solution:
The entrepreneur has to produce 2 metal and 4 plastic fasteners with cost of .
Explanation of Solution
Given:
- A design group has to produce at least six samples of fasteners.
- Cost of producing metal and plastic fasteners are respectively.
- Time of producing each metal and plastic fasteners are 4 hours and 2 hours respectively.
Calculation:
Begin by assigning symbols for the two variables.
be the number of metal fasteners produced.
be the number of plastic fasteners produced.
If be the total cost of producing fasteners,
The goal is to minimize subject to certain constraints on . Because represents number of fasteners, the only meaningful values of are non-negative.
Therefore, .
From the given data we get,
Therefore, the linear programming problem may be stated as,
Maximize, .
Subject to,
The graph of the constraints is illustrated in the figure below.
The corner points are as follows:
Corner points are | Value of objective function |
Therefore, the entrepreneur has to produce 2 metal and 4 plastic fasteners with cost of .
Chapter 11 Solutions
Precalculus
Additional Math Textbook Solutions
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus: Early Transcendentals (2nd Edition)
University Calculus: Early Transcendentals (3rd Edition)
Calculus & Its Applications (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Precalculus
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning