Download Cost Analysis for NASA Aquatics Lab: A Linear Programming Problem and more Study Guides, Projects, Research Introduction to Business Management in PDF only on Docsity!
Project Grant Team
John S. Pazdar Peter A. Wursthorn Project Director Principal Investigator Capital Comm-Tech College Capital Comm-Tech College Hartford, Connecticut Hartford, Connecticut
This project was supported, in part, by the Patricia L. Hirschy National Science Foundation Principal Investigator Opinions expressed are those of the authors Asnuntuck Comm-Tech College and not necessarily those of the Foundation Enfield, Connecticut
NASA - AMATYC - NSF
SPINOFFS
Spinoffs are relatively short learning modules inspired by the LTAs. They can be easily
implemented to support student learning in courses ranging from prealgebra through calculus.
The Spinoffs typically give students an opportunity to use mathematics in a real world context.
LTA - SPINOFF 2A Cost Analysis for the NASA Aquatics Lab
LTA - SPINOFF 2B NASA Aquatics Lab Loading
Ed Chandler - AMATYC Writing Team Member
Scottsdale Community College, Scottsdale, Arizona
Jerry Keepers - AMATYC Writing Team Member
University of Wisconsin Center - Fox Valley, Menasha, Wisconsin
(Currently at Potomac State College, West Virginia)
Reneé Ponik - NASA Scientist/Engineer
Kennedy Space Center, Florida
SPINOFF 2A
Cost Analysis for the NASA Aquatics Lab
Background Information
Governments and industries from around the world buy Shuttle space so that scientists can carry out experiments in a weightless environment. French and German scientists used space aboard the Shuttle Columbia for the August, 1997 launch and for several subsequent launches of other Shuttle flights. Their experiment studied the effects of weightlessness on fish and snails. When in orbit aboard a Shuttle craft, the animals are contained in a flexible spherical aquarium, and due to weightlessness, air forms in a pocket at the center of the aquarium.
An aquatics lab was built at Kennedy Space Center to perform preliminary experiments in preparation for the launch. Unused office space on the second floor of an existing building was modified to house racks of 30 and 50 gallon aquaria.
Technical Information
Capacity: The scientists were flexible on the number of 30 and 50 gallon aquaria, but they required at least 4,200 gallons total capacity.
Space: There was an area of 720 square feet available in the remodeled space for the aquaria. The aquaria were installed in racks stacked 3 high above the floor with another aquarium placed on the floor beneath the ones on the rack. Each rack of 30 gallon aquaria required 24 square feet of space and each rack of 50 gallon aquaria required 30 square feet of space.
Load: The second floor of the remodeled space had a load capacity of 200 pounds per square foot. Water weighs 8.34 pounds per gallon. Each metal rack for the 30 gallon aquaria adds an additional 200 pounds while each metal rack for the 50 gallon aquaria adds an additional 250 pounds to the weight of the water.
Cost: The cost of materials and installation of each 30 gallon rack was quoted as $2,600. Each 50 gallon rack was $4,500.
Student Task
Use linear programming techniques to do a cost analysis and determine the number of racks of 30 and 50 gallon aquaria which satisfy all the criteria and minimizes the cost.
Worksheet
Let x represent the number of 30 gallon racks used. Let y represent the number of 50 gallon racks used.
- Write a linear inequality in x and y which limits the total weight of all the racks and aquaria.
NASA - AMATYC - NSF
b) Figure 2
Evaluate the cost function defined in Exercise 4 above at each vertex of the compatibility region.
Use complete sentences to state your conclusion as to when the minimum cost is achieved.
NASA - AMATYC - NSF
