The Tamarisk Heritage Centre (a not-for-profit organization providing language and arts and crafts programs for children) receiv

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.

Response:

It is estimated that between 1100 and 1300 high school students in Detroit could obtain a gun if they desired to do so.

Rationale:

For the lower boundary, take 55% of 2000, which equals 0.55 × 2000 = 1100.

For the higher boundary, take 65% of 2000, equaling 0.65 × 2000 = 1300.

Therefore, the calculated range of students in Detroit who could obtain a firearm is from 1100 to 1300.

Answer:

To maximize utility, the consumption of product Y should be increased while reducing the intake of product X.

Explanation:

The utility-maximizing principle asserts that a consumer optimizes utility when the marginal utility per dollar spent is equal for both products.

For Product X, the marginal utility per dollar is:

= 2 utils per dollar

For Product Y, the marginal utility per dollar is:

= 8 utils per dollar

According to this principle, the consumer should increase the consumption of product Y and decrease that of product X.

Answer: The price elasticity of luxury weekend hotel packages in Las Vegas is -1.432.

Explanation:

The concept of price elasticity of demand assesses how much the quantity demanded changes in response to a price alteration of the product.

Mid point method-

The price elasticity of luxury weekend hotel packages in Las Vegas is -1.432.