Two roadway designs are under consideration for access to a permanent suspension bridge. Design 1A will cost $1.7 million to build and $175,000 per year to maintain. Design 1B will cost $3.6 million to build and $40,000 per year to maintain. Both designs are assumed to be permanent. Use an AW-based rate of return equation to determine (a) the breakeven ROR and (b) which design is preferred at an MARR of 25% per year.

Answer and Explanation:

A. Given that Design 1A will cost $1.7 million to build and $175,000 per year to maintain

Given that Design 1B will cost $3.6 million to build and $40,000 per year to maintain

Both designs are assumed to be permanent

To find ROR using AW based rate of return equation, we find present value of each design and equate them:

Each design is permanent so

Present value of perpetuity:

Design 1A= 1700000+175000/r

Design 1B = 3600000+40000/r

=1700000+175000/r=3600000+40000/r

135000/r=1900000

Cross multiply

r=135000/1900000

r= 0.0710

r=7.10%

B Given that ROR=7.10% and MARR is 25%

MARR>ROR

Hence we reject both designs

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.