XYZ Ltd produces medical equipment for the diagnosis of ARI disease in four factories. Four partner hospitals in Java Island have placed orders for production this month. The table below shows the cost of shipping each unit from each factory to each hospital, the number of units to be produced in each factory and the number of units ordered by each hospital. From Biaya pengiriman per unit (Jutaan Rupiah) Output (Ribuan) Hospital 1 Hospital 2 Hospital 3 Hospital 4 Pabrik 1 600 800 700 800 420 Pabrik 2 400 900 600 560 520 Pabrik 3 250 700 650 775 320 Pabrik 4 250 660 500 475 350 Total pesanan (ribuan) 345 345 620 300 XYZ Ltd Managers and Leaders aim to minimize total shipping costs by determining how many units will be delivered from each factory to each hospital. Based on this case: a) Formulate a linear programming model for this problem b) Determine the optimal solution of this model using the North West Corner, Vogel Method and Stepping-Stone transport methods! c) Make a dual equation for the case above and analyze the amount of shadow price using software!
XYZ Ltd produces medical equipment for the diagnosis of ARI disease in four factories. Four partner hospitals in Java Island have placed orders for production this month. The table below shows the cost of shipping each unit from each factory to each hospital, the number of units to be produced in each factory and the number of units ordered by each hospital.
|
From |
Biaya pengiriman per unit (Jutaan Rupiah) |
Output (Ribuan) |
|||
|
Hospital 1 |
Hospital 2 |
Hospital 3 |
Hospital 4 |
||
|
Pabrik 1 |
600 |
800 |
700 |
800 |
420 |
|
Pabrik 2 |
400 |
900 |
600 |
560 |
520 |
|
Pabrik 3 |
250 |
700 |
650 |
775 |
320 |
|
Pabrik 4 |
250 |
660 |
500 |
475 |
350 |
|
Total pesanan (ribuan) |
345 |
345 |
620 |
300 |
|
XYZ Ltd Managers and Leaders aim to minimize total shipping costs by determining how many units will be delivered from each factory to each hospital. Based on this case:
a) Formulate a linear programming model for this problem
b) Determine the optimal solution of this model using the North West Corner, Vogel Method and Stepping-Stone transport methods!
c) Make a dual equation for the case above and analyze the amount of shadow price using software!
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