In Problems 41-56, construct a mathematical model in the form of a linear programming problem. (The answer in the back of the book for these application problems include the model.) Then solve the problem using the simplex method. Include an interpretation of any nonzero slack variables in the optimal solution. Manufacturing: resource allocation. A small company manufactures three different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; component B requires 3 hours of fabrication and 1 hour of assembly; and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to 1 , 000 labor-hours of fabrication time and 800 labor-hours of assembly time available per week. The profit on each component, A , B , and C , is $ 7 , $ 8 , and $ 10 , respectively. How many components of each type should the company manufacture each week in order to maximize the profit (assuming that all components manufactured can be sold)? What is the maximum profit?
In Problems 41-56, construct a mathematical model in the form of a linear programming problem. (The answer in the back of the book for these application problems include the model.) Then solve the problem using the simplex method. Include an interpretation of any nonzero slack variables in the optimal solution. Manufacturing: resource allocation. A small company manufactures three different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; component B requires 3 hours of fabrication and 1 hour of assembly; and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to 1 , 000 labor-hours of fabrication time and 800 labor-hours of assembly time available per week. The profit on each component, A , B , and C , is $ 7 , $ 8 , and $ 10 , respectively. How many components of each type should the company manufacture each week in order to maximize the profit (assuming that all components manufactured can be sold)? What is the maximum profit?
Solution Summary: The author explains the linear programming problem model, if a company manufactures three components of computers.
In Problems 41-56, construct a mathematical model in the form of a linear programming problem. (The answer in the back of the book for these application problems include the model.) Then solve the problem using the simplex method. Include an interpretation of any nonzero slack variables in the optimal solution.
Manufacturing: resource allocation. A small company manufactures three different electronic components for computers. Component
A
requires
2
hours of fabrication and
1
hour of assembly; component
B
requires
3
hours of fabrication and
1
hour of assembly; and component
C
requires
2
hours of fabrication and
2
hours of assembly. The company has up to
1
,
000
labor-hours of fabrication time and
800
labor-hours of assembly time available per week. The profit on each component,
A
,
B
,
and
C
,
is
$
7
,
$
8
,
and
$
10
,
respectively. How many components of each type should the company manufacture each week in order to maximize the profit (assuming that all components manufactured can be sold)? What is the maximum profit?
Mathematics with Applications In the Management, Natural and Social Sciences (11th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.
Solve ANY Optimization Problem in 5 Steps w/ Examples. What are they and How do you solve them?; Author: Ace Tutors;https://www.youtube.com/watch?v=BfOSKc_sncg;License: Standard YouTube License, CC-BY
Types of solution in LPP|Basic|Multiple solution|Unbounded|Infeasible|GTU|Special case of LP problem; Author: Mechanical Engineering Management;https://www.youtube.com/watch?v=F-D2WICq8Sk;License: Standard YouTube License, CC-BY