Question

Module 9 q3Please put answer in BOLD. Will Upvote.

Consider the following pairwise comparison matrix for the price of three car models. Price Accord Taurus Cruz 1 Accord 1 1 3 5 1 Taurus 5 1 2 Cruz 3 2 1 Find the priorities after synthesization. (Round your answer to three decimal places.) Accord Taurus Cruz Compute the consistency ratio. (Use RI = 0.58. Round your answer to three decimal places.) Is this consistency ratio acceptable? --Select--- Since this consistency ratio is ---Select--- 0.10, the degree of consistency exhibited in the pairwise comparison matrix is

Answer 1

Given table : Accord Taurus Accord 1/5 Taurus 5 Cruz 3 cruz 1/3 2 By converting above table values in fractions into normal values as shown following. Taurus Accord Taurus cruz Total Accord 1.00 5.00 3.00 9.00 1.00 62 00 3.20 cruz 0:33 0.50 1.00 1-83 Now divide accord/a , Taurus/3.20 and cruz/1-83 we get as following. Accord Taurus cruz Accord Taurus 0-06 0.55 0.31 0.33 0.62 cruz 0.18 0.247 0:55 3 = 0.1016 Now take the average of each row. Accord = (0.11 to +0.06+0.18)/3. Taurus = = (0.55+0.31+0.27)|3 = (0.33+0.62 +0.55):3 = 0.500 0.3076 cruz

Hence we got cruz as top priority with value of 0.500. Taurus is and priority with value of 0.376 Accord is 3rd priority with value of 0.116. we have СТ consistency ratio RI CI= consistency index RI= Random index = 0.58 Also we have cI (Amax-n) + (n-1) where n= No of items need to compare. = 3 Here n=3 Now calculate the weighted sum by using priority weights. co.z C0.33 +0.376 1.0+ 0.116 0.50 = 0.500 5 3 ro.500 2 500 500 0.075 +0.376 0.752 + 11 0.038 0.058 o 116 11 -0.613 2-934 2.368

Now divide above weighted matrix by priority value we get Accord = (0.613 +0.116) = 5.28 Taurus = (2.934 + 0.376) = 7.80 Cruz = (2.368=0.500) =4.74 Amax = Average of above values. 528+7.80 +4.74 3 Amax = 5.94 c.I = (5.94-3) (3-1) C. I. = 1.47 C.R= 1.47 = 2.53 0.58 It consitency ratica to less than 107 is acceptable. Here it is 253% so it is acceptable