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Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
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Asmall manufacturing plant makes three types of
infiatable boats: one-person, two-person, and
four-person models. Each boat requires the services
of three departments, as listed in the table. The
cutting, assembly, and packaging departments have
available a maximum of 300, 140, and 184
labor-hours per week, respectively. Construct a
mathematical model to complete parts (A) through
(C) below. Use Gauss-Jordan elimination to solve
the model and then interpret the solution.
One-Person Two-Person
Boat
Four-Person
Department
Вoat
Boat
Cutting
0.3 hr
0.6 hr
0.9 hr
Assembly
0.2 hr
0.3 hr
0.4 hr
Packaging
0.1 hr
0.3 hr
0.6 hr
Construct a mathematical model that describes the plant operating at full capacity. Let the first, second, and third equations represent the cutting, assembly, and
packaging departments, respectively. Let x, represent the number of one-person boats, x, represent the number of two-person boats, and x, represent the number
of four-person boats.
1 +2 +I3 =
|X3 =
X, +
X3
%3D
(Type integers or decimals.)
Transcribed Image Text:Asmall manufacturing plant makes three types of infiatable boats: one-person, two-person, and four-person models. Each boat requires the services of three departments, as listed in the table. The cutting, assembly, and packaging departments have available a maximum of 300, 140, and 184 labor-hours per week, respectively. Construct a mathematical model to complete parts (A) through (C) below. Use Gauss-Jordan elimination to solve the model and then interpret the solution. One-Person Two-Person Boat Four-Person Department Вoat Boat Cutting 0.3 hr 0.6 hr 0.9 hr Assembly 0.2 hr 0.3 hr 0.4 hr Packaging 0.1 hr 0.3 hr 0.6 hr Construct a mathematical model that describes the plant operating at full capacity. Let the first, second, and third equations represent the cutting, assembly, and packaging departments, respectively. Let x, represent the number of one-person boats, x, represent the number of two-person boats, and x, represent the number of four-person boats. 1 +2 +I3 = |X3 = X, + X3 %3D (Type integers or decimals.)
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