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Linear Programming, Engineering Mathematics

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A company manufactures an assembly consisting of a frame, a shaft, and a ball bearing. The
company manufactures the shafts and frames but purchases the ball bearings from a ball bearing
manufacturer. Each shaft must be processed on a forging machine, a lathe, and a grinder. These
operations require 0.6 hour, 0.3 hour, and 0.4 hour per shaft, respectively. Each frame requires
0.8 hour on a forging machine, 0.2 hour on a drilling machine, 0.3 hour on a milling machine, and
0.6 hour on a grinder. The company has 5 lathes, 10 grinders, 20 forging machines, 3 drillers,
and 6 millers. Assume that each machine operates a maximum of 4500 hours per year. Formulate
the problem of nding the maximum number of assembled components that can be produced as a
linear program.


I have this solution:

Let x1 be the number of shafts that produced,
Let x2 be the number of frames that produced,
Let x3 be the number of ball bearings purchased.

Objective function is: maximize z=min(x1,x2,x3)

Constraints:

0.6 x1 + 0.8 x2 <= 4500 * 20

0.2 x2 <= 4500 * 3

0.3 x2 <= 4500 * 6

0.4 x1 + 0.6 x2 <= 4500 * 10

0.3 x1 <= 4500 * 5

But This is not an LP since it contains min(x1,x2,x3) in the objective function.
How can I make this linear, and Are my equations correct ? Please help me..

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