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 $6 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. Decision variables: X = number of wren houses to be produced Y = number of bluebird houses to be produced Z= 6X+ 15 Y a) Objective function: Subject to: 4X + 2Y 4X+ 12Y ≤ 48 (C₁) ≤ 120 (C₂) X, Y 20 b) On the graph on right, constraints C, and C₂ have been plotted. Using the point drawing tool, plot all the corner points for the feasible area. The optimum solution is: X = (round your response to two decimal places).

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FIND THE OPTIMUM SOLUTION TO

X=

Y=

MAX Z=

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 $6 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.
Decision variables:
X = number of wren houses to be produced
Y = number of bluebird houses to be produced
Z= 6 X+ 15 Y
a) Objective function:
Subject to:
4X + 2Y
4X+ 12Y
48 (C₁)
Ś 120 (C₂)
M
X, Y Z 0
b) On the graph on right, constraints C, and C₂ have been plotted.
Using the point drawing tool, plot all the corner points for the feasible area.
The optimum solution is:
X = (round your response to two decimal places).
CH
40
36-
32+
28-
24-
> 20
16-
12-
84
4
0
0
2
B.
F
A-
NY
A
8 12
16
20
X
tC₂
24 28 32
36
40
Transcribed Image Text: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 $6 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. Decision variables: X = number of wren houses to be produced Y = number of bluebird houses to be produced Z= 6 X+ 15 Y a) Objective function: Subject to: 4X + 2Y 4X+ 12Y 48 (C₁) Ś 120 (C₂) M X, Y Z 0 b) On the graph on right, constraints C, and C₂ have been plotted. Using the point drawing tool, plot all the corner points for the feasible area. The optimum solution is: X = (round your response to two decimal places). CH 40 36- 32+ 28- 24- > 20 16- 12- 84 4 0 0 2 B. F A- NY A 8 12 16 20 X tC₂ 24 28 32 36 40
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