ctions: Show calculations, state assumptions, and provide reference material as
ID: 1766436 • Letter: C
Question
ctions: Show calculations, state assumptions, and provide reference material as applicable. (6 pt) A 500 ft x 800 ft lot ill be used to construct a mutistory building with a customer irement of 350,000 ft? minimum of office foor space. The height of each story shal be 12 and maximum building height cannot exceed 150 feet. The parking lot outside the building st be at least 30 percent of the total floor area. The cost of the building in millions of dollars is roximated by C=15*h+.0005*A, where h is the height of the building in feet, and A is the ss-sectional area of the building per floor. Formulate the optimization problem. lution Form: d design variables and to the optimization subject to the following constraints: iterionExplanation / Answer
Let 'a' be the area of each floor of the building and 'n' be the number of floors.
Overall area of the plot is 800 x 500 ft2
1. The minimum office floor space required is 350,000 ft2
Total floor space in the building will be , n*a
i.e., na 350,000
2. The overall height of the building should not exceed 150 ft. and each floor is 12 ft high.
i.e.12n 150
3. 30% of the plot area is used for the parking lot, as such only 70% area is available for building construction.
thus the maximum available area is , 800 x 500 x 0.7 = 280,000 ft2
i.e., a 280,000
4. The cost equation of the building is
C = 0.15h+0.0005A, overall height is h = 12n
thus, C = 0.15*12n + 0.0005*a = 1.8n + 0.0005a
and we know cost is always to be minimized
4. As floor area and no. of floor cannot be negative
a, n 0
Hence, we can formulate the LPP as,
Let the design variables be a = floor area and n = no. of floors
Minimize C = 1.8n + 0.0005a
subject to the following constraints,
na 350,000
12n 150 OR n 12.5
a 280,000
a, n 0
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