Question

The Winston Company has four distribution centers (A, B, C, and D) that require 40,000, 70,000, 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 70,000 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: Wholesaler 1 2 3 A $1.90 $1.60 $1.80 Distribution Center B с $2.10 $1.60 $1.80 $2.10 $1.70 $2.00 D $1.90 $1.90 $1.80 a. Which of the following statements regarding setting up the tableau for the optimal solution for this problem is true? A. 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. The sum of supply capacities is less than the sum of demands, so a dummy wholesaler is needed. OC. The sum of supply capacities is greater than the sum of demands, so a dummy distribution center is needed. b. What is the total cost of the solution? The optimal cost is $. (Enter your response rounded to the nearest dollar.)

Answer 1

Answer:

a. A. The sum of supply capacities is equal to sum of demands, so no dummy wholesaler or distribution center is needed

It is a balance transportation problem where,

Total Supply = Total Demand = 190000 gallons

b.326

Excel LP Formation:

35 Distribution Center Cost Table 36 A D 1.90 1 37 38 Wholesaler $ $ $ 1.90 $ 1.60 $ 1.80 $ B 2.10 $ 1.80 $ 1.70 $ 2 C 1.60 $ 2.10 $ 2.00 $ 1.90 3 1.80 39 40 41 42 Distribution Center Supply - Demand Table 43 A B C D Total Supply 0 1 44 45 Wholesaler 46 2 0 50000 70000 70000 3 0 47 Total Demand 0 0 0 0 48 49 40000 70000 30000 50000 50 51 52 Objective $ 53 Min Cost 54

Formula:

A B C D E F H - 35 Cost Table Distribution Center C 36 A B D 37 1 1.9 2.1 1.9 1.6 2.1 38 Wholesaler 2 1.6 1.8 1.9 39 3 1.8 1.7 2 1.8 40 41 42 Distribution Center Supply - Demand Table Total Supply 43 A B с D 44 1 50000 45 Wholesaler 2 =SUM(C44:F44) =SUM(C45:F45) =SUM(C46:F46) 70000 70000 46 3 47 Total Demand I=SUM(C44:C46) =SUM(D44:046) I=SUM(E44:E46) =SUM(F44:F46) 48 49 40000 70000 30000 50000 50 51 52 Objective =SUMPRODUCT(C37:F39,C44:F46)/1000 53 Min Cost

Solver Parameters х Set Objective: SB553 To: Max Min O Value Of: 0 By Changing Variable Cells: $C$44:$F$46 Subject to the Constraints: $C$44:5F546 = integer SC$47:$F$47 = $C$49:$F$49 SG$44:$G$46 - $1$44:51546 Add Change Delete Reset All Load/Save Make Unconstrained variables Non-Negative Select a Solving Simplex LP Method: Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

Solution:

A B с D E F G H - $ $ $ Distribution Center A B с 1.90 $ 2.10 $ 1.60 $ 1.60 $ 1.80 $ 2.10 $ 1.80 $ 1.70 $ 2.00 $ D 1.90 1.90 1.80 35 Cost Table 36 37 1 38 Wholesaler 2 39 3 40 41 42 Supply - Demand Table 43 44 1 45 Wholesaler 2 Distribution Center D A 0 с 30000 20000 Total Supply 50000 70000 70000 50000 B 0 30000 40000 70000 40000 0 0 70000 46 3 0 0 30000 70000 47 Total Demand 40000 30000 50000 48 = = = 49 40000 70000 30000 50000 50 51 52 53 Min Cost Objective $ 326.00