Consider the following system:
Six trucks are used to haul coal from a mine to the rail road. There are two loaders and one weighing scale. After loading a truck immediately moves to the scale for weighing using FIFS policy. After weighing a truck begins a travel time and then returns to loader queue with the distribution of travel time as:
Travel time (Mins)
40
60
80
100
Probability
0.3
0.4
0.1
0.2
Further the distribution of loading time and weighing time are as:
Loading time (Mins)
5
10
15
Probability
0.5
0.3
0.2
Construct simulation table to trace the six trucks and:
(a) Compute average waiting time of loading
(b) Compute average time in system (loading and scaling times)
(c) Compute waiting probability for scaling
(d) Estimate the loader and scale utilization

i think this could be a possible answer (1 / 84) -1

good luck! : d

the value of x is 9 ⇒ answer b

step-by-step explanation:

* we can solve this problem using cosine and sine rule

- in δ abc

∵ ab = 36 , bc = 28 , ac = 16

- lets find the measure of angle b using the cosine rule

∵ cos b = [ab² + bc² - ac²]/2(ab)(bc)

∴ cos b = [36² + 28² - 16²]/2(36)(28)

∴ cos b = 19/21

∴ m∠b = cos^-1(19/21) ≅ 25°

- lets find the measure of angle a using the sine rule

∵ sina/bc = sinb/ac = sinc/ab

∴ sina/28 = sin25°/16 ⇒ by using cross multiplication

∴ sina = 28 × sin25°/16

∴ sina = 0.7396

∴ m∠a = sin^-1(0.7396) ≅ 48°

- from the figure m∠abd = m∠dbc

∵ m∠abc = 25°

∴ m∠abd = 25°/2 = 12.5°

- in δabd

∵ m∠a = 48° , m∠abd = 12.5°

∵ the sum of the measures of the interior angles of any δ is 180°

∴ m∠adb = 180° - (48° + 12.5°) = 119.5°

∵ ab = 36

∵ ad = x

- use the sine rule to find x

∵ sin∠adb/ab = sin∠abd/x

∴ sin119.5°/36 = sin12.5°/x ⇒ by using cross multiplication

∴ x = 36 × sin12.5°/sin119.5° = 8.95 ≅ 9

* the value of x is 9