Sensitivity analysis of a linear programming problem

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Question statement

A factory manufractures two products, X and Y. Existing demand means the factory must produce at least {minimum_x} units of product X and {minimum_y} units of product Y.

A unit of X requires {x_resource[0]} units of resource 1 and {x_resource[1]} units of resource 2.

A unit of Y requires {y_resource[0]} units of resource 1 and {y_resource[1]} units of resource 2.

Each unit of product X sold earns £{profit_x} profit, and each unit of product Y sold earns £{profit_y} profit.

Give any introductory information the student needs.

			Name	Type	Generated Value

			Name	Type	Generated Value

product_baseline	number	6000
x_bound	integer	5100
y_bound	integer	7800
resource_baseline	list	[ 624000, 70200 ]
profit_baseline	number	10

			Name	Type	Generated Value

			x_intercept_a	list	[ 3315, 2040 ]
			y_intercept_a	list	[ 3666, 3354 ]

			Name	Type	Generated Value

minimum_x	integer	1020
minimum_y	integer	1248
x_resource	list	[ 215, 34 ]
y_resource	list	[ 201, 15 ]
total_resource	list	[ 955281, 84817 ]
profit_x	integer	5
profit_y	integer	5

			Name	Type	Generated Value

x_intercept	list	[ 955281/215, 84817/34 ]
y_intercept	list	[ 318427/67, 84817/15 ]
inequality_coordinates	list	Nested 2×3 list

			Name	Type	Generated Value

program	list	List of 8 items
best	number	1
line_is_binding	list	[ false, true, true, false ]
best_coords	list	[ 1020, 3342.4666666667 ]
binding_lines	list	[ 1, 2 ]

			Name	Type	Generated Value

line_names	list	List of 4 items
change_description	string	is doubled
line_prepositions	list	Nested 2×4 list

			Name	Type	Generated Value

nonbinding_line	integer	0
change	integer	2
changing_affects_solution	boolean	false

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
10^random(1..3)*random(2..8)

JME function reference

Description

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Generated value: `number`

6000

→ Used by:

profit_x
profit_y
x_bound
y_bound

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Advice

a)

The optimal solution is found at the intersection of the lines representing {line_names[binding_lines[0]]} and {line_names[binding_lines[1]]}. These constraints are binding; the other constraints are non-binding.

b)

If the {line_names[nonbinding_line]} {change_description}, the optimal solution found earlier ends up {line_prepositions[1][nonbinding_line]} the line representing the {line_names[nonbinding_line]}, making it invalidis still {line_prepositions[0][nonbinding_line]} the line representing the {line_names[nonbinding_line]}, so the optimal solution is not affected.

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Sensitivity analysis of a linear programming problem

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Taxonomy: mathcentre

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Taxonomy: Context

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History

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

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Generated value: `number`

Parts

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a)

b)

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Sensitivity analysis of a linear programming problem

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Information only

a)

b)

Generated value: `number`