Question

Weldex Industries begins to manufacture a newly designed, small, spot welding machine. The labour hours required for making the second and third units are 29.7 and 28.3 hours respectively.

The labour hours required to manufacture the first unit are close to

32.3 hours

33.9 hours

27.3 hours

30.7 hours

the labour hours required to manufacture the 50^th unit are close to

Select one:

17.2 hours

21.2 hours

19.3 hours

20.2 hours

If labour costs are $18/hour, the total labour costs to produce the first four machines are close to

Select one:

$2117

$2071

$2066

$1954

Answer 1

Time for 1st unit = T

Time for 2nd unit = 29.7 = T*(2)^b

Time for 3rd unit = 28.3 = T*(3)^b

Equating the two equations for T and finding b:

29.7/28.3 = 2^b/3^b

1.05*3^b = 2^b

Taking natural Log on both sides

Ln(1.05*3^b) = Ln(2^b)

Ln1.05 + b*Ln3 = b*Ln2

0.04879 + b*1.099 = b*0.693

b = -0.1203

29.7 = T*2^-0.1203

T = 32.3 Hours

1) 32.3

2) Time for 50th unit = 32.3*(50)^-0.1203 = 20.2 hours

3) Time for 4th unit = 32.3*(4)^-0.1203 = 27.3 hours

Time for 1st 4 units = 32.3 + 29.7 + 28.3 + 27.3 = 117.6 hours

Total labor cost = Total time for 1st 4 unit*Labor rate = 117.6*18 = 2117 $

Ans - 2117