United Research Associates (URA) had received a contract to produce two units of
ID: 466356 • 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 3,750 hours and cost $19,500 in materials and equipment usage. Labor cost is charged at $25 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.
What will be the average time for the 20 missile guidance controls? (Round your answer to the nearest whole number.)
What will the average cost be for guidance control for the 20 in the contract? (Round your answer to the nearest dollar amount.)
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 3,750 hours and cost $19,500 in materials and equipment usage. Labor cost is charged at $25 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.
Explanation / Answer
Labor Hours
Cost per unit
1st unit
5000
$30,000
2nd unit
3750
$19,500
Learning %
3750/5000 = 0.75 = 75%
19500/30000 = 0.65 = 65%
a.
Labor hours required for Nth control = TN = T1*C
TN = number of labor-hours required to produce the Nth unit
T1 = number of labor-hours required to produce the first unit
C = learning-curve coefficient found in Exhibit 6.4 for Learning %
Labor hours required for 22nd control = T22
For 22nd unit at 75% learning curve, C = 0.2772
Labor hours required for 22nd control = T22 = 5000 x 0.2772
T22 = 1386 hours
Material and machine cost estimation for 22nd control = C22
For 22nd unit at 65% learning curve, C = 0.1465
Material and machine cost estimation for 22nd control = T22 = $30,000 x 0.1465
C22 = $4,395
Total Cost Required for 22nd control = $25 x T22 + C22
= $25 x 1368 + $4,395
= $38,595
Total Cost Required for last unit (22nd control) = $38,595
b.
What will be the average time for the 20 missile guidance controls?
Total time for building next 20 control = Total time required for 22 control – total time required for 2 control
Total time required for N control = TN = T1 x CT
TN = Total Time required to produce the N unit
T1 = number of labor-hours required to produce the first unit
CT = Cumulative learning-curve coefficient found in Exhibit 6.5 for Learning %
Total time required for 22 control = T22 = T1 x CT
For 22 units at 75% learning curve, CT = 9.388
T22 = T1 x CT = 4000 x 9.388 = 37,552 hours
Total time required for 2 control = T2 = T1 x CT
For 2 units at 75% learning curve, CT = 1.750
T22 = T1 x CT = 4000 x 1.750 = 7,000 hours
Total time for building next 20 control = T22 – T2 = 37552 – 7000 = 30552
Average time for the 20 missile guidance controls = 30,552/20 = 1527.6 hours
c.
What will the average cost be for guidance control for the 20 in the contract?
Total materials and machine cost estimation for N control = CN = C1 x CT
CN = materials and machine cost required to produce the N unit
T1 = materials and machine cost of producing the first unit
CT = Cumulative learning-curve coefficient found in Exhibit 6.5 for Learning %
Total materials and machine cost required for 22 controls = C22 = C1 x CT
For 22 units at 65% learning curve, CT = 6.492
T22 = T1 x CT = $30,000 x 6.492 = $194,760
Total materials and machine cost required for 2 controls = C2 = C1 x CT
For 2 units at 65% learning curve, CT = 1.650
C2 = C1 x CT = $30,000 x 1.750 = $49,500
Total materials and machine cost building next 20 control = C22 – C2 = $194,760 – $49,500 = $145,260
Average materials and machine cost for the 20 missile guidance controls = $145,260/20 = $7,263hours
Average cost be for guidance control for the 20 in the contract
= Average Labor Cost + Average materials and machine cost
= Average hours req. x Labor cost + $7,263
= 1527.6 x $25 + $7,263
= $45,453
Average cost be for guidance control for the 20 in the contract = $45,453
Labor Hours
Cost per unit
1st unit
5000
$30,000
2nd unit
3750
$19,500
Learning %
3750/5000 = 0.75 = 75%
19500/30000 = 0.65 = 65%
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