A new highway is to be constructed. Design A calls for a concrete pavement costing $80 per foot with a 20​-year life; four paved ditches costing $3 per foot​ each; and two box culverts every​ mile, each costing $9,000 and having a 20​-year life. Annual maintenance will cost ​$1,800 per​ mile; the culverts must be cleaned every five years at a cost of $350 each per mile. Design B calls for a bituminous pavement costing $55 per foot with a 10​-year life; three sodded ditches costing $1.45 per foot​ each; and four pipe culverts every​ mile, each costing $2,100 and having a 10​-year life. The replacement culverts will cost $2,350 each. Annual maintenance will cost ​$2,900 per​ mile; the culverts must be cleaned yearly at a cost of $215 each per​ mile; and the annual ditch maintenance will cost  $1.35 per foot per ditch. Compare the two designs on the basis of equivalent worth per mile for a 20​-year period. Find the most economical design on the basis of AW and PW if the MARR is 6​% per year.

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A new highway is to be constructed. Design A calls for a concrete pavement costing $80 per foot with a 20​-year life; four paved ditches costing $3 per foot​ each; and two box culverts every​ mile, each costing $9,000 and having a 20​-year life. Annual maintenance will cost
​$1,800 per​ mile; the culverts must be cleaned every five years at a cost of
$350 each per mile. Design B calls for a bituminous pavement costing $55
per foot with a 10​-year life; three sodded ditches costing $1.45 per foot​ each; and four pipe culverts every​ mile, each costing $2,100 and having a 10​-year life. The replacement culverts will cost $2,350 each. Annual maintenance will cost ​$2,900 per​ mile; the culverts must be cleaned yearly at a cost of $215 each per​ mile; and the annual ditch maintenance will cost
 $1.35 per foot per ditch.
Compare the two designs on the basis of equivalent worth per mile for a 20​-year period. Find the most economical design on the basis of AW and PW if the MARR is 6​% per year.
Reference
Discrete Compounding; i=6%
Single Payment
Compound
Uniform Series
Sinking
Fund
Compound
Present
Worth
Сapital
Recovery
Factor
Present
Amount
Amount
Worth
Factor
Factor
Factor
Factor
To Find P
Factor
To Find F
To Find F
Given A
To Find P
To Find A
To Find A
Given F
PIE
Given P
Given A
Given F
Given P
FIP
FIA
PIA
AIF
AIP
0.9434
1.0600
1.1236
1
1.0000
2.0600
3.1836
4.3746
0.9434
1.0000
1.0600
0.5454
0.8900
1.8334
2.6730
0.4854
3
0.3741
1.1910
1.2625
0.8396
0.3141
4
0.7921
3.4651
0.2286
0.2886
4.2124
0.1774
0.1434
0.1191
5
1.3382
0.7473
0.7050
5.6371
0.2374
1.4185
6.9753
8.3938
9.8975
4.9173
5.5824
0.2034
7
1.5036
1.5938
0.6651
0.1791
8.
0.6274
6.2098
0.1010
0.1610
6.8017
7.3601
1.6895
0.5919
0.5584
11.4913
0.0870
0.1470
10
1.7908
13.1808
0.0759
0.1359
7.8869
8.3838
8.8527
9.2950
9.7122
11
1.8983
0.5268
14.9716
0.0668
0.1268
12
2.0122
0.4970
16.8699
0.0593
0.1193
13
2.1329
0.4688
0.4423
18.8821
0.0530
0.1130
14
2.2609
21.0151
0.0476
0.0430
0.1076
15
2.3966
0.4173
23.2760
0.1030
16
2.5404
0.3936
25.6725
10.1059
0.0390
0.0354
0.0990
2.6928
0.3714
10.4773
10.8276
11.1581
17
28.2129
0.0954
18
2.8543
0.3503
30.9057
0.0324
0.0924
19
3.0256
0.3305
33.7600
0.0296
0.0896
20
3.2071
0.3118
36.7856
11.4699
0.0272
0.0872
Print
Done
Transcribed Image Text:Reference Discrete Compounding; i=6% Single Payment Compound Uniform Series Sinking Fund Compound Present Worth Сapital Recovery Factor Present Amount Amount Worth Factor Factor Factor Factor To Find P Factor To Find F To Find F Given A To Find P To Find A To Find A Given F PIE Given P Given A Given F Given P FIP FIA PIA AIF AIP 0.9434 1.0600 1.1236 1 1.0000 2.0600 3.1836 4.3746 0.9434 1.0000 1.0600 0.5454 0.8900 1.8334 2.6730 0.4854 3 0.3741 1.1910 1.2625 0.8396 0.3141 4 0.7921 3.4651 0.2286 0.2886 4.2124 0.1774 0.1434 0.1191 5 1.3382 0.7473 0.7050 5.6371 0.2374 1.4185 6.9753 8.3938 9.8975 4.9173 5.5824 0.2034 7 1.5036 1.5938 0.6651 0.1791 8. 0.6274 6.2098 0.1010 0.1610 6.8017 7.3601 1.6895 0.5919 0.5584 11.4913 0.0870 0.1470 10 1.7908 13.1808 0.0759 0.1359 7.8869 8.3838 8.8527 9.2950 9.7122 11 1.8983 0.5268 14.9716 0.0668 0.1268 12 2.0122 0.4970 16.8699 0.0593 0.1193 13 2.1329 0.4688 0.4423 18.8821 0.0530 0.1130 14 2.2609 21.0151 0.0476 0.0430 0.1076 15 2.3966 0.4173 23.2760 0.1030 16 2.5404 0.3936 25.6725 10.1059 0.0390 0.0354 0.0990 2.6928 0.3714 10.4773 10.8276 11.1581 17 28.2129 0.0954 18 2.8543 0.3503 30.9057 0.0324 0.0924 19 3.0256 0.3305 33.7600 0.0296 0.0896 20 3.2071 0.3118 36.7856 11.4699 0.0272 0.0872 Print Done
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