8. (a) A manufacturer has two products P1
and , P2
both of which are produced in two steps
by machines M1
and . M2
The process time per hundred for the products on the
machines
M1 M2
Profit (in
thousand Rs.
per 100 units)
P1
4 5 10
P2
5 2 5
Available
hours
100 80
The manufacturer can sell as much as he can produce of both products. Formulate the
problem as LP model. Determine optimum solution, u
Solution:
Let the units of product 1 produced be and the units of product 2 produced be .
Rs.1000 per 100 units, or Rs. 10 per 1 unit.
Objective function, maximise
subject to constraints:
Now, plotting these inequations on graph, we get:
Here, OABC is the feasible region.
Corner points are
At
At
At
At
Clearly, maximum occurs at .
Thus, the optimal solution is Rs. 6470.58 when units of product 1 and units of product 2 are produced.
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