Sensitivity analysis of a linear programming problem

Error

There was an error loading the page.

Contributors

Newcastle University Mathematics and Statistics

History

○

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Created this.

There is only one version of this question that you have access to.

There are 3 other versions that do you not have access to.

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	7000
x_bound	integer	5810
y_bound	integer	25200
resource_baseline	list	[ 504000, 226800 ]
profit_baseline	number	1000

			Name	Type	Generated Value

			x_intercept_a	list	[ 4997, 1685.3 ]
			y_intercept_a	list	[ 8316, 16128 ]

			Name	Type	Generated Value

minimum_x	integer	930
minimum_y	integer	4536
x_resource	list	[ 98, 166 ]
y_resource	list	[ 102, 9 ]
total_resource	list	[ 939244, 299090 ]
profit_x	integer	6
profit_y	integer	8

			Name	Type	Generated Value

x_intercept	list	[ 469622/49, 149545/83 ]
y_intercept	list	[ 469622/51, 299090/9 ]
inequality_coordinates	list	Nested 2×3 list

			Name	Type	Generated Value

program	list	List of 8 items
best	number	0
line_is_binding	list	[ true, false, true, false ]
best_coords	list	[ 930, 8314.7450980392 ]
binding_lines	list	[ 0, 2 ]

			Name	Type	Generated Value

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

			Name	Type	Generated Value

nonbinding_line	integer	1
change	rational	1/2
changing_affects_solution	boolean	true

			Name	Type	Generated Value

Automatically regenerate variables?

Name

Data type

Value

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

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `number`

7000

→ Used by:

profit_x
profit_y
x_bound
y_bound

Information only

Ask the student a question, and give any hints about how they should answer this part.

Graph goes here

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.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Information only
Match choices with answers
Match choices with answers		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet

This question is used in the following exams:

Loading...

Error

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)

Loading...

Error

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`