Answer:
the probability of the consumer’s shopping in location 1 is 50.6 %
the probability of the consumer’s shopping in location 2 is 29.9 %
the probability of the consumer’s shopping in location 3 is 19.4 %
Explanation:
Huff’s law is a mathematical model that takes consideration in the relation between the patronage and distance from location of the shopping area.
The equation for this mathematical model can be expressed as :
[tex]P_y = \dfrac{\dfrac{ S_j}{(T_y)^{\lambda} } }{ \sum \limits ^{n}_{f} \dfrac{S_j}{(T_y)^{\lambda }}}[/tex]
Where;
[tex]P_y=[/tex]Probability of a consumer travelling from home (i) to shopping location (j)
[tex]T_y[/tex] = Travel time from consumer’s home (i) to shopping location (j)
[tex]\lambda[/tex] = Dataset used to determine the effect of travel time in different kinds of shopping trips
n = Number of different shopping location.
NOW; from the given information.
for location 1 , the consumer shopping probability is :
[tex]P_{i, 1} = \dfrac{ \dfrac{15000}{(12)^2} }{ \dfrac{15000}{(12)^2} + \dfrac{20000}{(18)^2} + \dfrac{25000}{(25)^2}}[/tex]
[tex]P_{i, 1} = \dfrac{ \dfrac{15000}{144} }{ \dfrac{15000}{144} + \dfrac{20000}{324} + \dfrac{25000}{625} }[/tex]
[tex]P_{i, 1} = \dfrac{104.17 }{ 104.17 + 61.73 +40.00 }[/tex]
[tex]P_{i, 1} = \dfrac{104.17 }{ 205.9 }[/tex]
[tex]\mathbf{P_{i,1} = 0.506 \ or \ 50.6 \% }[/tex]
Thus; the probability of the consumer’s shopping in location 1 is 50.6 %
for location 2 , the consumer shopping probability is :
[tex]P_{i, 2} = \dfrac{ \dfrac{20000}{(18)^2} }{ \dfrac{15000}{(12)^2} + \dfrac{20000}{(18)^2} + \dfrac{25000}{(25)^2} }[/tex]
[tex]P_{i, 2} = \dfrac{ \dfrac{20000}{324} }{ \dfrac{15000}{144} + \dfrac{20000}{324} + \dfrac{25000}{625} }[/tex]
[tex]P_{i, 2} = \dfrac{61.73 }{ 104.17 + 61.73 +40.00 }[/tex]
[tex]P_{i, 2} = \dfrac{61.73 }{ 205.9 }[/tex]
[tex]\mathbf{P_{I,2} = 0.299 \ or \ 29.9 \%}[/tex]
Thus; the probability of the consumer’s shopping in location 2 is 29.9 %
for location 3 , the consumer shopping probability is :
[tex]P_{i, 3} = \dfrac{ \dfrac{25000}{(25)^2} }{ \dfrac{15000}{(12)^2} + \dfrac{20000}{(18)^2} + \dfrac{25000}{(25)^2} }[/tex]
[tex]P_{i, 3} = \dfrac{ \dfrac{25000}{625} }{ \dfrac{15000}{144} + \dfrac{20000}{324} + \dfrac{25000}{625} }[/tex]
[tex]P_{i, 3} = \dfrac{40.00 }{ 104.17 + 61.73 +40.00 }[/tex]
[tex]P_{i, 3} = \dfrac{40.00}{ 205.9 }[/tex]
[tex]\mathbf{P_{i,3} = 0.194 \ or \ 19.4 \%}[/tex]
Thus; the probability of the consumer’s shopping in location 3 is 19.4 %
