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Soal $1$ . Terdapat demand dan supply yang tidak seimbang. Hitunglah biaya terkecil transportasi menggunakan penyeimbangan terlebih dahulu. Selanjutnya lakukan langkah metode north west corner. $\newline$ \begin{tabular}{|c|c|c|c|c|} $\newline$ \hline & D $1$ & D $2$ & D $3$ & Supply \\ $\newline$ \hline $81$ & $15$ & $5$ & $10$ & $20$ \\ $\newline$ \hline $\mathrm{S} 2$ & $10$ & $5$ & $10$ & $25$ \\ $\newline$ \hline $83$ & $20$ & $10$ & $15$ & $30$ \\ $\newline$ \hline Demand & $45$ & $20$ & $35$ & \\ $\newline$ \hline $\newline$ \end{tabular}

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Math Problems

Algebra 1

Multiply and divide rational expressions

Full solution

Q. Soal

1

. Terdapat demand dan supply yang tidak seimbang. Hitunglah biaya terkecil transportasi menggunakan penyeimbangan terlebih dahulu. Selanjutnya lakukan langkah metode north west corner.

\newline

\begin{tabular}{|c|c|c|c|c|}

\newline

\hline & D

1

& D

2

& D

3

& Supply \\

\newline

\hline

81

15

5

10

20

\newline

\hline

\mathrm{S} 2

10

5

10

25

\newline

\hline

83

20

10

15

30

\newline

\hline Demand &

45

20

35

& \\

\newline

\hline

\newline

\end{tabular}

Balance Supply and Demand: : Balance the total supply and total demand to see if they are equal. $\newline$ Total Supply = $20 + 25 + 30 = 75$ . $\newline$ Total Demand = $45 + 20 + 35 = 100$ . $\newline$ Since Total Supply is not equal to Total Demand, we need to add a dummy supply to balance it.
Add Dummy Supply: : Add a dummy supply row with the difference between total demand and total supply. $\newline$ Dummy Supply needed = Total Demand - Total Supply = $100 - 75 = 25$ . $\newline$ Now, add this dummy supply to the table.
Apply North West Corner: : Apply the North West Corner method to the balanced table. $\newline$ Allocate as much as possible to the North West corner cell $D1, S1$ without exceeding supply or demand. $\newline$ Allocation for $D1, S1$ = $\min(45, 20) = 20$ .
Update Supply and Demand: : Update the supply and demand after the allocation. $\newline$ New Supply for $S_1 = 20 - 20 = 0$ . $\newline$ New Demand for $D_1 = 45 - 20 = 25$ .
Move to Next Cell: : Move to the next cell in the row $(D2, S1)$ and allocate as much as possible. $\newline$ Since the supply for $S1$ is now $0$ , we move down to the next supply row $(D1, S2)$ . $\newline$ Allocate for $D1, S2 = \min(25, 25) = 25$ .
Continue North West Corner: : Update the supply and demand after the allocation. $\newline$ New Supply for $S_2 = 25 - 25 = 0$ . $\newline$ New Demand for $D_1 = 25 - 25 = 0$ .
Allocate Remaining Demand: : Continue with the North West Corner method for the remaining cells. $\newline$ Allocate for $D_2, S_2 = \min(20, 0) = 0$ , but since $S_2$ supply is $0$ , move to $S_3$ . $\newline$ Allocate for $D_2, S_3 = \min(20, 30) = 20$ .
Allocate to Dummy Supply: : Update the supply and demand after the allocation. $\newline$ New Supply for $S_3 = 30 - 20 = 10$ . $\newline$ New Demand for $D_2 = 20 - 20 = 0$ .
Calculate Total Cost: : Allocate for $D3$ , $S3$ = $\min(35, 10) = 10$ . Update the supply and demand after the allocation. New Supply for $S3$ = $10 - 10 = 0$ . New Demand for $D3$ = $35 - 10 = 25$ .
Calculate Total Cost: : Allocate for D $3$ , S $3$ = $\min(35, 10) = 10$ . Update the supply and demand after the allocation. New Supply for S $3$ = $10 - 10 = 0$ . New Demand for D $3$ = $35 - 10 = 25$ .: Allocate the remaining demand to the dummy supply. Allocate for D $3$ , Dummy = $\min(25, 25) = 25$ . Update the supply and demand after the allocation. New Supply for Dummy = $25 - 25 = 0$ . New Demand for D $3$ = $25 - 25 = 0$ .
Calculate Total Cost: : Allocate for D $3$ , S $3$ = $\min(35, 10) = 10$ . Update the supply and demand after the allocation. New Supply for S $3$ = $10 - 10 = 0$ . New Demand for D $3$ = $35 - 10 = 25$ .: Allocate the remaining demand to the dummy supply. Allocate for D $3$ , Dummy = $\min(25, 25) = 25$ . Update the supply and demand after the allocation. New Supply for Dummy = $25 - 25 = 0$ . New Demand for D $3$ = $25 - 25 = 0$ .: Calculate the total transportation cost using the allocations and the given costs. Total Cost = $(20 \times 81) + (25 \times 15) + (20 \times 20) + (10 \times 10) + (25 \times 0)$ . Total Cost = $1620 + 375 + 400 + 100 + 0$ . Total Cost = $1620 + 375 + 400 + 100$ . Total Cost = $2495$ .