MathDB

You want to hang a weight

P

so that it is

7

m below a ceiling. To do this, it is suspended by means of a vertical cable attached to the midpoint

M

of a chain hung by its ends from two points on the ceiling

A

and

B

distant from each other

4

m. The price of the cable

PM

p

pta/m and that of the chain

AMB

q

pta/m. It is requested: a) Determine the lengths of the cable and the chain to obtain the lowest price cost of installation. b) Discuss the solution for the different values of the relation

p/q

of both prices. (It is assumed that the weight is large enough to be considered rectile lines the chain segments

AM

and

MB

4

Problems(1)