The Winston Company has four distribution centers (A, B, C, and D) that require 40,000, 60,000, 30,000, and 50,000 gallons of de-ionized water, respectively, per month for cleaning their long-haul trucks. Three de-ionized water wholesalers (1, 2, and 3) indicated their willingness to supply as many as 50,000, 70,000, and 60,000 gallons, respectively. The total cost (shipping plus price) of delivering 1,000 gallons of de-ionized water from each wholesaler to each distribution center is shown in the following table: Distribution Center B C Wholesaler A D 1 $1.70 $1.90 $1.60 $1.70 2 $1.90 $1.60 $1.70 $1.40 $1.60 3 $1.50 $1.80 $1.40 a. Which of the following statements regarding setting up the tableau for the optimal solution for this problem is true? OA. The sum of supply capacities is greater than the sum of demands, so a dummy distribution center is needed. OB. The sum of supply capacities is less than the sum of demands, so a dummy wholesaler is needed. C. The sum of supply capacities equals the sum of demands, so no dummy wholesaler or distribution center is needed. The capacity is fully utilized and the demand is fully satisfied. b. What is the total cost of the solution? The optimal cost is $. (Enter your response rounded to the nearest dollar.)
The Winston Company has four distribution centers (A, B, C, and D) that require 40,000, 60,000, 30,000, and 50,000 gallons of de-ionized water, respectively, per month for cleaning their long-haul trucks. Three de-ionized water wholesalers (1, 2, and 3) indicated their willingness to supply as many as 50,000, 70,000, and 60,000 gallons, respectively. The total cost (shipping plus price) of delivering 1,000 gallons of de-ionized water from each wholesaler to each distribution center is shown in the following table: Distribution Center B C Wholesaler A D 1 $1.70 $1.90 $1.60 $1.70 2 $1.90 $1.60 $1.70 $1.40 $1.60 3 $1.50 $1.80 $1.40 a. Which of the following statements regarding setting up the tableau for the optimal solution for this problem is true? OA. The sum of supply capacities is greater than the sum of demands, so a dummy distribution center is needed. OB. The sum of supply capacities is less than the sum of demands, so a dummy wholesaler is needed. C. The sum of supply capacities equals the sum of demands, so no dummy wholesaler or distribution center is needed. The capacity is fully utilized and the demand is fully satisfied. b. What is the total cost of the solution? The optimal cost is $. (Enter your response rounded to the nearest dollar.)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:The Winston Company has four distribution centers (A, B, C, and D) that require 40,000, 60,000, 30,000, and 50,000 gallons of de-ionized water, respectively, per
month for cleaning their long-haul trucks. Three de-ionized water wholesalers (1, 2, and 3) indicated their willingness to supply as many as 50,000, 70,000, and
60,000 gallons, respectively. The total cost (shipping plus price) of delivering 1,000 gallons of de-ionized water from each wholesaler to each distribution center is
shown in the following table:
Distribution Center
Wholesaler
A
B
1
$1.70
$1.90
$1.60
$1.70
2
$1.40
$1.90
$1.60
$1.70
3
$1.60
$1.50
$1.80
$1.40
a. Which of the following statements regarding setting up the tableau for the optimal solution for this problem is true?
O A. The sum of supply capacities is greater than the sum of demands, so a dummy distribution center
needed,
O B. The sum of supply capacities is less than the sum of demands, so a dummy wholesaler is needed.
C. The sum of supply capacities equals the sum of demands, so no dummy wholesaler or distribution center is needed. The capacity is fully utilized and the
demand is fully satisfied.
b. What is the total cost of the solution?
The optimal cost is $. (Enter your response rounded to the nearest dollar.)
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