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A large apartment building is to be built using modular con- struction techniques. The arrangement of apartments on any particular floor is to be chosen from one of three basic floor plans. Plan A has 18 apartments on one floor, including 3 three-bedroom units, 7 two-bedroom units, and 8 one- bedroom units. Each floor of plan B includes 4 three-bedroom units, 4 two-bedroom units, and 8 one-bedroom units. Each floor of plan C includes 5 three-bedroom units, 3 two-bedroom units, and 9 one-bedroom units. Suppose the building contains a total of x1 floors of plan A, x2 floors of plan B, and x3 floors of plan C. a. What interpretation can be given to the vector x7 ? 8 b. Write a formal linear combination of vectors that expresses the total numbers of three-, two-, and one-bedroom apart- ments contained in the building. c. [M] Is it possible to design the building with exactly 66 three-bedroom units, 74 two-bedroom units, and 136 one- bedroom units? If so, is there more than one way to do it? Explain your answer.

A large apartment building is to be built using modular con- struction techniques. The arrangement of apartments on any particular floor is to be chosen from one of three basic floor plans. Plan A has 18 apartments on one floor, including 3 three-bedroom units, 7 two-bedroom units, and 8 one- bedroom units. Each floor of plan B includes 4 three-bedroom units, 4 two-bedroom units, and 8 one-bedroom units. Each floor of plan C includes 5 three-bedroom units, 3 two-bedroom units, and 9 one-bedroom units. Suppose the building contains a total of x1 floors of plan A, x2 floors of plan B, and x3 floors of plan C. a. What interpretation can be given to the vector x7 ? 8 b. Write a formal linear combination of vectors that expresses the total numbers of three-, two-, and one-bedroom apart- ments contained in the building. c. [M] Is it possible to design the building with exactly 66 three-bedroom units, 74 two-bedroom units, and 136 one- bedroom units? If so, is there more than one way to do it? Explain your answer.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.3: Rules For Addition
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Construction Plan: Question # 5: A large apartment building is to be built using modular con- struction techniques. The arrangement of apartments on any particular floor is to be chosen from one of three basic floor plans. Plan A has 18 apartments on one floor, including 3 three-bedroom units, 7 two-bedroom units, and 8 one- bedroom units. Each floor of plan B includes 4 three-bedroom units, 4 two-bedroom units, and 8 one-bedroom units. Each floor of plan C includes 5 three-bedroom units, 3 two-bedroom units, and 9 one-bedroom units. Suppose the building contains a total of x1 floors of plan A, x2 floors of plan B, and x3 floors of plan C. a. What interpretation can be given to the vector x 7 ? 8 b. Write a formal linear combination of vectors that expresses the total numbers of three-, two-, and one-bedroom apart- ments contained in the building. c. [M] Is it possible to design the building with exactly 66 three-bedroom units, 74 two-bedroom units, and 136 one- bedroom units? If so, is there more than one way to do it? Explain your answer.
Transcribed Image Text:Construction Plan: Question # 5: A large apartment building is to be built using modular con- struction techniques. The arrangement of apartments on any particular floor is to be chosen from one of three basic floor plans. Plan A has 18 apartments on one floor, including 3 three-bedroom units, 7 two-bedroom units, and 8 one- bedroom units. Each floor of plan B includes 4 three-bedroom units, 4 two-bedroom units, and 8 one-bedroom units. Each floor of plan C includes 5 three-bedroom units, 3 two-bedroom units, and 9 one-bedroom units. Suppose the building contains a total of x1 floors of plan A, x2 floors of plan B, and x3 floors of plan C. a. What interpretation can be given to the vector x 7 ? 8 b. Write a formal linear combination of vectors that expresses the total numbers of three-, two-, and one-bedroom apart- ments contained in the building. c. [M] Is it possible to design the building with exactly 66 three-bedroom units, 74 two-bedroom units, and 136 one- bedroom units? If so, is there more than one way to do it? Explain your answer.
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