Figure 4 illustrates a railway built from city P and Q at 0 degree, branching off at the point Q to R. Due to the poor land surface from P to R, the point Q must be located at least 10 km to the south P. If the construction works need RM 50 000 per kilometer between P and Q and RM 25 000 per kilometer from Q to R, determine the location of point Q and branch angle e so that the overall construction cost is minimum. Then, prove that this location gives the absolute minimum construction cost. 10 km R 20 km Figure 4
Figure 4 illustrates a railway built from city P and Q at 0 degree, branching off at the point Q to R. Due to the poor land surface from P to R, the point Q must be located at least 10 km to the south P. If the construction works need RM 50 000 per kilometer between P and Q and RM 25 000 per kilometer from Q to R, determine the location of point Q and branch angle e so that the overall construction cost is minimum. Then, prove that this location gives the absolute minimum construction cost. 10 km R 20 km Figure 4
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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Question
![Figure 4 illustrates a railway built from city P and Q at 0 degree, branching off at the point
Q to R. Due to the poor land surface from P to R, the point Q must be located at least 10
km to the south P. If the construction works need RM 50 000 per kilometer between P and
Q and RM 25 000 per kilometer from Q to R, determine the location of point Q and branch
angle e so that the overall construction cost is minimum. Then, prove that this location gives
the absolute minimum construction ocost.
10 km
Q
R
20 km
Figure 4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff6ce6ec-e13a-486c-95f5-150bcd840484%2F856d76a4-7b91-45e6-8977-4e76fb039eb1%2F2hfu2tv_processed.png&w=3840&q=75)
Transcribed Image Text:Figure 4 illustrates a railway built from city P and Q at 0 degree, branching off at the point
Q to R. Due to the poor land surface from P to R, the point Q must be located at least 10
km to the south P. If the construction works need RM 50 000 per kilometer between P and
Q and RM 25 000 per kilometer from Q to R, determine the location of point Q and branch
angle e so that the overall construction cost is minimum. Then, prove that this location gives
the absolute minimum construction ocost.
10 km
Q
R
20 km
Figure 4
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