A sales representative needs to design a display booth for trade shows. Because

Question

A sales representative needs to design a display booth for trade shows. Because trade show organizers typically charge for floor space at their shows, the booth is to be 100 square feet. The booth is to be 6 feet tall and three-sided, with the back of the booth made of display board and the two sides of the booth made of gathered fabric. The display board for the back of the booth costs $40 per square foot. The fabric costs $2 per square foot and needs to be twice the length of the side to allow for gathering.

Calculate the minimum cost of constructing a booth according to these specifications. (Round your answer to the nearest cent.) _____________

What should be the dimensions of the booth? (Round your answers to three decimal places.)

Width of booth _________ feet

Length of side wall _______ feet

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Please provide answers in detail

Explanation / Answer

a)

let back length=x

then side=100/x

height=6

back area =6x

side area= 100*6/x

cost= 40*6*x+ 2*6*4*100/x

diff. w.r.t x and pitting =0 gives

x=4.472

hence cost=$ 2146.63

b)width of booth =x= 4.472 ft

c)length of side walls =100/4.472=22.361 ft

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