Problem 6-10 United Research Associates (URA) had received a contract to produce
ID: 390821 • Letter: P
Question
Problem 6-10
United Research Associates (URA) had received a contract to produce two units of a new cruise missile guidance control. The first unit took 5,000 hours to complete and cost $40,000 in materials and equipment usage. The second took 3,750 hours and cost $34,000 in materials and equipment usage. Labor cost is charged at $32 per hour.
The prime contractor has now approached URA and asked to submit a bid for the cost of producing another 20 guidance controls. Use Exhibit 6.4 and Exhibit 6.5.
a. What will the last unit cost to build? (Round your answer to the nearest dollar amount.)
b. What will be the average time for the 20 missile guidance controls? (Round your answer to the nearest whole number.)
c. What will the average cost be for guidance control for the 20 in the contract? (Round your answer to the nearest dollar amount.)
exhibit 6.4 Improvement Curves: Table of Unit Values excel 1.0000 1.0000 .0000 1.0000 .0000 .0000 1.0000 1.0000 r500 8000 8500 6000 6500 4150 5052 5682 6338 021 72 8162 9219 3600 4225 9 5625 6400 225 8100 9025 304 368 4368 1 59 6r 2670 3281 2383 29B4 3674 21602/46 .3430 .4219 .5120 .6141 1880 2552 3228 4017 9000 9500 5345 6337 7439 885 5874 7161 1802 2135 8 .3o65 4493 b84 6854 8320 1130 276 5386 6696 8145 8074 28 3812 854 6312 8012 3164 3013 344 1554 1465 203 772 397 2674 4747 6169 7904 190 2629 3548 470 17372437 334 45 5776 1605 2286 3184 1498 2163 3050 4211 5708 7611 1410 2060 3 1336 1216 1010 5607 7545 0560 0879 0489 0785 0437 1972 2838 2676 3829 5367 2547 2440 3579 5137 7486 1715 033 0610 0987 1545 2349 3482 5046 7168 0336 0572 0935 1479 .2271 .3397 496 7112 1287 .2038.3139 418.6937 160 0237 0427 0T34 1217 1952 3042 4623 6869 6809 2887 4469 6757 022 .04640788 1879 2959 0201 0371 0655 .0323 .0584 149 0289 0531 1109 2740 1504 2625 4202 .6557 350 .0133 0262 0491 .08791517 2532 4105 .6482 1453 1399 2387 3951 1352 2329 .38886314 12r5 2232 3/82 6229 2454 600 .0090 0188 03/2 0r03 800 .0073 015 03210624 1163 2088 3620 .6098 900 .006 0146 0302 1119 2029 .3056 6045 0062 .0137 1,200 0054 .0122.026O 0527 1897 3404 .5918 1,400 0048 01110240 095 09 1 1830 3325 5850 1,800 0040 .0095 0211 0446 089 1725 3200 5743 2,000 003 0377 0178 3,000 002 .0069 0162 0350 r60 1930 .2961.530Explanation / Answer
Given are following details :
Time of completion of first unit = 5000 units
Time of completion of second unit = 3750
Therefore , Learning rate for production time = 3750/5000 x 100 = 75 %
Cost of first unit = $40,000
Cost of second unit = $34,000
Therefore, Learning rate for cost of material = 34,000/40,000 x 100 = 85%
To know details of cost of producing another 20 units, we need to find out total cost of 2 ( initial number of units ) + 20 ( new units ) = 22 units
Answer to question # a :
Labour hours required for the last unit i.e. 22nd unit = 1386.16 hours
Labour cost = $32/ hour
Therefore, Labour cost = $32 x 1386.16 = $44357 ( rounded to nearest whole number )
Material cost required for last unit I.e. 22nd unit = $19378
Last unit cost to build = $19378
= Labour cost + Material cost
= $44357 + $19378
= $63735
Last unit cost to build = $63735
Answer to question #b :
Total time required for producing 22 missile controls = 46941 hours
Total time required for producing 2 units = 8750 hours
Therefore , total time required for 20 missile guidance control
= 46941 – 8750 hours
= 38191 hours
Average time for 20 missile guidance control
= 38191/ 20hours
= 1909.55 hours
Average time for 20 missile guidance control = 1909.55 hours
Answer to question # c :
Labour cost of making 20 missile guidance control = $32 / hour x 18097 hours = $579104
Material cost for 20 missile guidance control
= Cumulative cost of first 22 missile guidance control – Cumulative cost of first 2 missile guidance control
= $535060 - $74000
= $461060
Total cost of making 20 missile guidance control
= Total labour cost + Total material cost
= $579104 + $461060
= $1040164
Average cost of 20 missile guidance control = $1040164 / 20 = $52008.20
AVERAGE COST OF 20 MISSILE GUIDANCE CONTROL = $52008.20
Last unit cost to build = $63735