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dimulka
9 days ago
8

Burrito King (a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fa

st-food establishments. The Burro-Master 9000 requires a constant 30 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 45 seconds. To help determine the amount of space needed for the line at the drive-up window
A. What is the average line length (in cars)?

B. What is the average number of cars in the system (both in line and at the window)?

C. What is the expected average time in the system?
Business
1 answer:
marusya05 [3.4K]9 days ago
3 0

Response:

(A)0.6600 (B) 1.325 (C) 0.997 or 1 minute

Clarification:

Resolution

It's provided that:

The fixed production time = 30 seconds

The customer arrival time determined by the Poisson distribution is = 45 seconds

Now,

(A) We calculate the typical line length of vehicles

The formula is as follows:

Lq = λ²/ 2μ ( μ -λ)

In this equation,

λ = signifies the average arrival rate

μ = denotes the average service rate

We first determine the average arrival rate as shown below:

The average arrival rate λ = arrival rate/ 60 seconds

= 60/45

= 1.33 customers per minute

Next, we find the average service rate which is detailed below

The average service rate μ = 60 seconds/ average rate

= 60/30 = 2 customers per minute

Now we will calculate the average line length in vehicles as shown here:

Lq = λ²/ 2μ ( μ -λ)

Lq = 1.33²/2*2 (2-1.33)

Lq = 1.7689/4 (0.67)

Lq = 1.7689/2.68

Lq = 0.6600

Thus, the average line length for vehicles is 0.6600 cars

(B) We calculate the average number of vehicles in the entire system

Ls = Lq + λ /μ

Ls = 0.600 + 1.33/2

Ls = 0.6600 + 0.665

Ls = 1.325

(C) Lastly, we need to ascertain the expected average duration in the system outlined here:

Ws = Ls/λ

Ws= 1.325/1.33 = 0.997 or 1.00

The predicted average duration in the system is 0.997 or 1.00 minutes.

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Explanation:

From the information in the question:

Price for a 12-oz can = 75 cents = $0.75

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To find the cost per ounce for the can = $0.75 divided by 12

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The overall expenditure for transporting the containers to the U.S. amounts to $2,594,930

Explanation:

Consider the following details about Company WWG:

Total Current volume (CBM) = 190,000

Percentage shipped directly = 0.89

Volume shipped directly (CBM) = 169,100

Volume at consolidation center = 190,000 - 169,100 = 20,900

To compute the shipping expenses for the company as outlined below:

Shipping Cost calculations

Direct shipping by Container type (in Feet) 20 40

Volume (%) 0.21 0.79

Volume (CBM) = 169,100*0.21 =169,100*0.79

= 35,511 =133,589

Container capacity utilized 85% 85%

Container center by container type

Volume (%) = 100

Volume (CBM) = 20,900

Container capacity used = 96%

Container capacity (CBM) (34)

Containers shipped = 35,511/ (34*0.85) = 1,229

Shipping Cost per container = $480

Shipping Costs by container size ($) = 1,229*480 = $589,920

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Containers shipped = 133,589/ (0.85*67) + 20,900/ (0.96*67) = 2,671

Shipping Cost per container = $600

Shipping Costs by container size ($) = 2,671*600 = $1,602,600

Calculate the total shipping cost as follows:

Total shipping fees = $589,920 + $1,602,600 = $2,192,520

Determine the operating costs for the consolidation center as follows:

Number of centers = 4

Annual fixed cost per center = $75,000

Total annual fixed costs = $75,000*4 = $300,000

Variable cost per CBM = $4.9

Total annual variable cost = 20,900*$4.9 = $102,410

Total annual consolidation center expenses = $300,000+$102,410 = $402,410

Now compute the complete cost of moving containers to the U.S. as below:

Total Cost = Total Shipping Fees + Total Annual Consolidation center Expense

= $2,192,520 + $402,410

= $2,594,930

Thus, the entire cost involved in shipping the containers to the U.S. is $2,594,930.

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Earl Miller, owner of a Papa Gino's franchise, wants to buy a new delivery truck in 6 years. He estimates the truck will cost $3
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Answer:

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