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A craftsman named William Barnes builds two kinds of ​birdhouses, one for wrens and a second for bluebirds. Each wren birdhouse takes 4 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and   12 units of lumber. The craftsman has available 48 hours of labor and 120 units of lumber. Wren houses yield a profit of $8 each and bluebird houses yield a profit of $15 each.   The aim of the objective function for William should be to Maximize   the objective value. Part 2 Decision​ variables:                                                X​ = number of wren houses to be produced                                                Y​ = number of bluebird houses to be produced Part 3 ​a) Objective​ function:   Z= 8   8X+15   15Y     Part 4 Subject​ to:     4X+2Y less than or equals≤   48 ​(C1​) Part 5     4X+12Y less than or equals≤   120 ​(C2​) Part 6     ​X, Y ≥0     Part 7 ​b) On the graph on​ right, constraints C1 and C2 have been plotted.   Using the point drawing tool​, plot all the corner points for the feasible area.   Part 8 The optimum solution​ is: Part 9 X​ = enter your response here   ​(round your response to two decimal​ places).

A craftsman named William Barnes builds two kinds of ​birdhouses, one for wrens and a second for bluebirds. Each wren birdhouse takes 4 hours of labor and 4 units of lumber. Each bluebird house requires 2 hours of labor and   12 units of lumber. The craftsman has available 48 hours of labor and 120 units of lumber. Wren houses yield a profit of $8 each and bluebird houses yield a profit of $15 each.   The aim of the objective function for William should be to Maximize   the objective value. Part 2 Decision​ variables:                                                X​ = number of wren houses to be produced                                                Y​ = number of bluebird houses to be produced Part 3 ​a) Objective​ function:   Z= 8   8X+15   15Y     Part 4 Subject​ to:     4X+2Y less than or equals≤   48 ​(C1​) Part 5     4X+12Y less than or equals≤   120 ​(C2​) Part 6     ​X, Y ≥0     Part 7 ​b) On the graph on​ right, constraints C1 and C2 have been plotted.   Using the point drawing tool​, plot all the corner points for the feasible area.   Part 8 The optimum solution​ is: Part 9 X​ = enter your response here   ​(round your response to two decimal​ places).

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Question
A craftsman named William Barnes builds two kinds of
​birdhouses, one for wrens and a second for bluebirds. Each wren birdhouse takes
4
hours of labor and
4
units of lumber. Each bluebird house requires
2
hours of labor and  
12
units of lumber. The craftsman has available
48
hours of labor and
120
units of lumber. Wren houses yield a profit of
$8
each and bluebird houses yield a profit of
$15
each.
 
The aim of the objective function for William should be to
Maximize
 
the objective value.
Part 2
Decision​ variables:
                                               X​ = number of wren houses to be produced
                                               Y​ = number of bluebird houses to be produced
Part 3
​a) Objective​ function:
 
Z=
8
 
8X+15
 
15Y
 
 
Part 4
Subject​ to:
 
 
4X+2Y
less than or equals≤
 
48
​(C1​)
Part 5
 
 
4X+12Y
less than or equals≤
 
120
​(C2​)
Part 6
 
 
​X, Y
≥0
 
 
Part 7
​b) On the graph on​ right, constraints
C1
and
C2
have been plotted.  
Using the point drawing
tool​,
plot all the corner points for the feasible area.
 
Part 8
The optimum solution​ is:
Part 9
X​ =
enter your response here
 
​(round your response to two decimal​ places).
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