Linear Programming problem

2015-01-25 7:11 am
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)????

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
似乎題目應該還有其他資料要提供?


收錄日期: 2021-04-15 18:01:55
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20150124000051KK00116

檢視 Wayback Machine 備份