Assume that there are three shopping locations with 500,1,000,and 3,000 square feet of space allocated to outdoor lighting fixtures.A group of potential customers lives 5 minutes from the first location,10 minutes from the second location,and 15 minutes from the third location.The retailer estimates the effect of travel time to be 2.The probability of consumers' shopping at location two is ________.
A) 7 percent
B) 10 percent
C) 15 percent
D) 23 percent

Question

Quizplus · Accepted Answer

The probability of consumers shopping at a location can be calculated using the Huff Model, which considers both the attractiveness of a location (in this case, square footage) and the travel time to the location. The formula for the Huff Model is:$$ P_i = \frac{A_i / T_i^{\beta}}{\sum_{n=1}^{N} (A_n / T_n^{\beta})} $$Where:- $P_i$ is the probability of shopping at location $i$,- $A_i$ is the attractiveness of location $i$ (square footage for this example),- $T_i$ is the travel time to location $i$,- $\beta$ is the parameter for the effect of travel time (given as 2 in this example),- $N$ is the total number of locations.Given:- $A_1 = 500$, $T_1 = 5$,- $A_2 = 1000$, $T_2 = 10$,- $A_3 = 3000$, $T_3 = 15$,- $\beta = 2$.Plugging the values into the formula:$$ P_2 = \frac{1000 / 10^2}{(500 / 5^2) + (1000 / 10^2) + (3000 / 15^2)} $$$$ P_2 = \frac{1000 / 100}{(500 / 25) + (1000 / 100) + (3000 / 225)} $$$$ P_2 = \frac{10}{(20) + (10) + (13.33)} $$$$ P_2 = \frac{10}{43.33} $$$$ P_2 \approx 0.23 $$Therefore, the probability of consumers shopping at location two is approximately 23 percent.

Assume That There Are Three Shopping Locations with 500,1,000,and 3,000