United Research Associates (URA) had received a contract to produce two units of
ID: 388514 • Letter: U
Question
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 4,750 hours and cost $34,000 in materials and equipment usage. Labor cost is charged at $20 per hour.
The prime contractor has now approached URA and asked to submit a bid for the cost of producing another 20 guidance controls.
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.)
Explanation / Answer
We will use Learning curve table to arrive at required result .
Given are following details :
Time of completion of first unit = 5000 units
Time of completion of second unit = 4750
Therefore , Learning rate for production time = 4750/5000 x 100 = 95 %
Cost of first unit = $40,000
Cost of second unit = $50,000
Therefore, Learning rate for cost of material = 40,000/50,000 x 100 = 80%
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
Labour cost = $20 / hour
Therefore, Labour cost = 3977.68 x 20 = $79553.60 ( $79554 rounded to nearest whole number )
Material cost required for last unit I.e. 22nd unit = $19378
Last unit cost to build
= Labour cost + Material cost
= $79554 + $19378
= $98932
Last unit cost to build = $98932
2)Total time required for producing 22 missile controls = 93620.26 hours
Total time required for producing 2 units = 9750 hours
Therefore , total time required for 20 missile guidance control
= 93620.26 – 9750 hours
= 83870.26
Average time for 20 missile guidance control
= 83870.26/20 hours
= 4193.51 hours ( 4194 hours rounded to nearest whole number )
Average time for 20 missile guidance control = 4194 hours
3)Total labour cost of making 20 missile guidance control
= $20 / hour x Total time required for 20 missile guidance control
= $20 x 83870.26
= $1677405.20
Total material cost for 22 units = $535059.58
Total material cost for first 2 units = $74000
Therefore , total material cost to build 20 missile guidance control
= $535059.58 - $74,000
= $461059.58
Total cost of making 20 missile guidance control
=( Total labour cost + Total material cost ) of making 20 missile guidance control
= $1677405.20 + $461059.58
= $2138464.78
Average cost of guidance control for the 20 in the contract
= Total cost of making 20 missile guidance control / 20
= $2138464.78/20
= $106923.24 ( $106923 rounded to nearest $ amount)
Average cost for 20 guidance control in the contract = $106923
Last unit cost to build = $98932
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