Answer :

Let the dealer buy x fans and y sewing machines. The LPP is to maximize profit Z = 22x + 18y


Subject to constraints:


x + y ≤ 20


360x + 240y ≤ 5760


3x + 2y ≤ 48 and x ≥ 0, y ≥ 0


First we draw the lines AB and CD whose equations are x + y = 20



And 3x + 2y = 48




The feasible region is OBPCO which is shaded in the above figure.


P is the point of intersection of the lines x + y = 20 and 3x + 2y = 48.


Solving these equations, we get the point P (8, 12).


The vertices of the feasible region are O (0, 0), B (0, 20), P (8, 12), C (16, 0)


The value of objective function Z = 22x + 18y at these vertices are as follows:



The maximum profit is Rs. 392 when 8 fans and 12 sewing machines are purchased.


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