Question

4. Find the labor cost to produce 40 cellphones if the time needed to pro- duce the first cellphone is 120 hours and the learning rate is 90%. Assume the labor rate is $11/hour. 5- A famous burger restaurant would like to determin te for their employees. By conducting time studies, they determined that time required for the first sandwich is 35 minutes and the eighth first sandwich is 35 minutes and the eighth sandwich manager find the learning rate for their employees. is 25 minutes. Help the manager find the learning rate for their

hi. could you please help me solve this problem for practice. step by step solving will be appreciated.
thanks

Answer 1

4.

The Learning rate of 90% means that if the first cellphone is produced in 120 hours,the second would be produced in 120*90% = 108 hours,the fourth cellphone in 108*90% = 97.20 hours and so on.

The formula to compute the time taken to produce any one unit would be as under :

Assuming "x" as the unit number & T(x) = Time taken to produce the xth unit

T(x) = Time taken to produce the 1st unit * Learning rate ^(log(x)/log(2))

Values given in the question

Learning Rate = 90%

Time taken to produce 1 st unit = 120 hours

The solution is being presented in the table below :

Learning Rate	90%
Unit No	Unit Time (Hours)	Cumulative Time
1	120.00	120.00
2	108.00	228.00
3	101.54	329.54
4	97.20	426.74
5	93.96	520.70
6	91.39	612.09
7	89.27	701.37
8	87.48	788.85
9	85.93	874.77
10	84.56	959.34
11	83.35	1,042.68
12	82.25	1,124.93
13	81.26	1,206.19
14	80.35	1,286.54
15	79.51	1,366.05
16	78.73	1,444.78
17	78.01	1,522.79
18	77.33	1,600.12
19	76.70	1,676.82
20	76.11	1,752.93
21	75.54	1,828.48
22	75.01	1,903.49
23	74.51	1,977.99
24	74.03	2,052.02
25	73.57	2,125.59
26	73.13	2,198.72
27	72.71	2,271.43
28	72.31	2,343.74
29	71.93	2,415.67
30	71.56	2,487.23
31	71.20	2,558.43
32	70.86	2,629.29
33	70.53	2,699.82
34	70.21	2,770.02
35	69.90	2,839.92
36	69.60	2,909.53
37	69.31	2,978.84
38	69.03	3,047.87
39	68.76	3,116.63
40	68.50	3,185.13

Total time taken to produce 40 units of cellphones is 3185.13 hours

Labor Rate is $ 11 per hours

Total Labor Cost to produce 40 cellphones is 3185.13 * $ 11 = $ 35,036.43

5.

Value given in the question are as under:

Time taken to produce 1st sandwich = 35 minutes

Time taken to produce 8th sandwich = 25 minutes

We need to find the Learning rate by using these values in the formula  

=> T(x) = Time taken to produce the 1st unit * Learning rate ^(log(x)/log(2)) ,where T(x) is the time taken to produce the x th unit

T(8) = 35 min* Learning Rate ^(log(8)/log(2))

25 min = 35 min*Learning Rate^(log(8)/log(2))

[We will put the logarithmic value of 8 and 2 in the above mentioned equation: log 8 = 2.0794415 and log 2 = 0.6931472]

25 = 35* Learning Rate ^( 2.0794415/0.6931472)

Learning Rate ^ 3 = 25/30

Learning Rate ^ 3 = 0.7142857 (Learning Rate raised to the power 3 is the derived value)

Learning Rate = (0.7142857)^(1/3) (to derive Learning rate we need to derive the cube root of the value)

Learning Rate = 0.8939035

Learning Rate = 89.39035%