A bank of 10 machines requires regular periodic service. Machine running time and service time are both exponential. what is the optimal number of operators for this bank of machines

hello your question lacks some details below is the complete question

A bank of 10 machines requires regular periodic service. Machine running time and service time are both exponential. Machines run for an average of 44 minutes between service requirements, and service time averages six minutes per machine

If operators cost $15 per hour in wages and fringe benefits and machine downtime costs $75 per hour in lost production, what is the optimal number of operators for this bank of machines?

A 1

B 2

C 3

D 4

E 5

Answer : 3 operators ( c )

Explanation:

number of machines = 10

machine run time for each = 44 minutes

service time = 6 minutes

cost of each operator = $15 per hour

loss during machine down time = $75 per hour

hence the optimal number of operators  

The total minutes the machine would work in a hour

= (60 - 6) * 10 = 540 minutes  

assuming we assign 180 minutes to each operator then each operator would cost = 15 * 3 = $45

for three operators that would be = 45 * 3 = $135

lost inquired during down time

= 6 minutes * 10 = 60 minutes  i.e the total cost inquired per hour = $75

hence 3 operators would be an optimal number of operators because the operators would work lesser hours and more efficiently as well

bd = 9 cm

step-by-step explanation:

in a 30°-60°-90° triangle, the ratio of side lengths is 1 : √3 : 2. that is, the longest side (hypotenuse) is twice the length of the shortest side.

all of the triangles in your geometry are 30°-60°-90° triangles. ac is the hypotenuse of δacd, and the short side of δabc.

the short side ad of δacd will be half the length of ac, so 3 cm. the hypotenuse ab of δabc will be twice the length of ac, so 12 cm. segment bd is the difference of the lengths ab and ad, so is

bd = ab -ad

bd = 12 cm - 3 cm = 9 cm

comment on side length ratios

you can figure the ratios of side lengths in a 30°-60°-90° triangle by considering the trig ratios of the angles. or you can figure the length of the altitude of an equilateral triangle of side length 2 using the pythagorean theorem.

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