United Research Associates (URA) had received a contract to produce two units of
ID: 393651 • 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 $30,000 in materials and equipment usage. The second took 4,500 hours and cost $24,000 in materials and equipment usage. Labor cost is charged at $20 per hour. The company expects “learning” to occur relative to labor and also relative to the pricing of materials and equipment.
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.)
Cost of last unit $
b. What will be the average time for the 20 missile guidance controls? (Round your answer to the nearest whole number.)
Average time hours
c. What will the average cost be for guidance control for the 20 in the contract? (Round your answer to the nearest dollar amount.)
Average cost $
Use the table of cumulative values and table of unit values (improvement curves). please also follow the roundings stated in the questions
Explanation / Answer
Learning rate can be calculated as :
= Time or cost to make 2nd unit / Time or cost to make 1st unit x 100
We will use Learning curve table to arrive at required result .
Given are following details :
Time of completion of first unit = 5000 hours
Time of completion of second unit = 4500 hours
Therefore , Learning rate for production time = 4500/5000 x 100 = 90%
Cost of first unit = $30,000
Cost of second unit = $24,000
Therefore, Learning rate for cost of material = 24000/30000 x 100 = 80%
Answer to question # a :
After making 2 guidance controls, one needs to produce another 20 guidance control. Therefore , last unit in this case will be the 22nd unit
Labour hours required for the last unit i.e. 22nd unit = 3125.49 hours
Labour cost = $20/ hour
Therefore, Labour cost = $20/ hour x 3125.49 hours = $ 62509.80
Material cost required for last unit I.e. 22nd unit = $11090.67
Last unit cost to build = Labour cost + Material cost = $62509.80 + $11090.67 = $73600.47 ( $ 73600 rounded to nearest whole number )
Last unit cost to build = $73600
Answer to question #b :
Total time required for producing 22 missile controls = 79312 hours
Total time required for producing 2 units = 9500 hours
Therefore , total time required for 20 missile guidance control = 79312 – 9500 hours = 69812 hours
Average time for 20 missile guidance control = 69812 / 20 = 3490.60 hours ( 3491 hours rounded to nearest whole number )
Average time for 20 missile guidance control = 3491 hours
Answer to question # c :
Total labour cost of making 20 missile guidance control
= $20 / hour x Total time required for 20 missile guidance control ( as derived in #b)
= $20 x 69812
= $ 1396240
Total material cost for 22 units = $336897
Total material cost for first 2 units = $54000
Therefore , total material cost to build 20 missile guidance control = $336897 - $54000 = $282897
Total cost of making 20 missile guidance control
=(Total labour cost+ Total material cost ) of making 20 missile guidance control
= $1396240 + $282897
= $ 1679137
Average cost of guidance control for the 20 in the contract
= Total cost of making 20 missile guidance control / 20
= $1679137/20
= $ 83956.85 ( $83957 rounded to nearest whole number )
Average cost for 20 guidance control in the contract = $83957
Last unit cost to build = $73600
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