A pharmaceutical factory has two warehouses, East House and West House, each of which currently stores 140 tonnes and 40 tonnes of medicine respectively. Two drugstores, Healthy Store and Heal Store, place orders of 100 tonnes and 50 tonnes of medicine respectively. Healthy Store is 60 km from East House and 30 km from West House. Heal Store is 80 km from East House and 20 km from West House. The cost of transporting 1 tonne of medicine is $1/km. Suppose x tonnes and y tonnes of medicine are transported from East House to Healthy Store and Heal Store respectively.
(a) Write down all the constraints on x and y.
Ans :
0 <= x <= 100 ..........(1)
0 <= y <= 50 ............(2)
x+y >= 110 ...............(3)
x+y <= 140 ...............(4)
How to get (3)????
Linear Programming problem
2015-01-25 7:11 am
回答 (2)
2015-01-25 5:40 pm
✔ 最佳答案
a) Suppose x tonnes and y tonnes of medicine are transported from East House to Healthy Store and Heal Store respectively.So, (100-x) tonnes and (50-y) tonnes of medicine are transported from West House to Healthy Store and Heal Store respectively.0 <= x <= 100 ............... (1)0 <= y <= 50 ................. (2)For West House, (100-x) + (50-y) <= 40ie. x+y >= 110 ............... (3)For East House, x+y <= 140 .................... (4)
[Transportation fee, for Healthy Store,$60x + $30(100-x)= $(3000 + 30x)For Heal Store,$80y + $20(50-y)= $(1000 + 60y)]
2015-01-25 09:57:18 補充：
Intersection points of (x, y) are (100, 10), (100, 40), (60, 50) (90, 50).
Minimum transportation fee occurs when (x, y) is (100, 10). ie.
$(3000 + 30*100 + 1000 + 60*10)
= $7600
Maximum transportation fee is :
$(3000 + 30*90 + 1000 + 60*50)
= $9700
2015-01-25 09:59:11 補充：
I think part (b) is to calculate the minimum cost of transporting,
so the answer is $7600.
2015-01-25 7:44 am
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