Optimization Problems: Fire Safety 1. According to fire safety codes, a potentia

Question

Optimization Problems: Fire Safety 1. According to fire safety codes, a potential exit window needs to be at least 20 inches wide, at least 24 inches tall, and at least 5.7 square feet in area. a) If a window is 20" wide X 24"tall, does it meet the requirements for safety? b) How tall would a 20" wide window have to be to meet code? c) How wide would a 24" tall window have to be to meet code? d) You are designing low-cost housing units, and need to economize on the cost of the windows. If every bedroom in a housing unit requires a potential exit window that is up to code, and the glass costs $3.18 per square foot, what will be the minimum cost per window? e) The window framing material costs $1.42 per linear foot. Assuming that each window will have an area of exactly 5.7 square feet, write a formula for the total cost per window of frame and glass. f) What is the total minimum cost for one window?

Explanation / Answer

According to Chegg's guideline, we are required to do only 4 parts of a question

A. A 20” wide and 24” tall window won't be able to meet the code as area of this window will be 3.22 square foot( 20*24 = 480” = 3.22 foot) which is less 5.7 square foot.

B. 20” = 1.66 foot

For 20” wide window area must be at least 5.7 foot.

Height of window = 5.7/1.66 = 3.43 foot

= 41.16 inch atleast.

C. 24” = 2 foot.

Width = 5.7/2 = 34.2 atleast.

D. Minimum area according to code is 5.7 square foot.

Minimum cost = 5.7 * 3.18 = $ 18.12 per window.

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