A locally owned department store samples two customers in each of five geo-graphic areas to estimate consumer spending in its home appliances department. It is estimated that these customers are a good sample of the 10,000 customers the store serves. The number of customers in each area is C ₁ = 1,500, C ₂ = 2,500, C ₃ = 1,000, C ₄ = 3,000, and C = 5 2,000. It is found that the two consumers have the following budgets in dollars for home appliances per year: B₁₁ = 100, B 12 = 150; B ₂₁ = 75, B ₂₂ = 100; B _{31 =} 125, B ₃₂ = 125; B ₄₁ = 100, B ₄₂ = 120; and B ₅₁ = 120, B ₅₂ = 125.

a. Using the Huff retail location model, estimate annual home appliance sales for the store.

b. Bull’s- Eye, a chain department store, opens a branch in a shopping complex near by. The Bull’s- Eye branch is three times larger than the locally owned store. The travel times in minutes from the five areas to the two stores ( j = 1 for the locally owned store, j = 2 for Bull’s- Eye) are T ₁₁ = 20, T _{12 =} 15; T ₂₁ = 35, T ₂₂ = 20; T ₃₁ = 30, T ₃₂ = 25; T ₄₁ = 20, T ₄₂ = 25; and T ₅₁ = 25, T _{52 =} 25. Use the Huff retail location model to estimate the annual consumer expenditures in the home appliance section of each store assuming that l = 1.