Q. 95.0( 1 Vote )

A cottage industr

Answer :

let the cottage industry manufacture x number of pedestal lamps and y number of wooden shades.

x and y ≥ 0


The given information can be represented in the following tabular form:



The profit on lamps is Rs 5 and that on the shades is Rs 3.


The constraints are 2x + y ≤ 12


And 3x + 2y ≤ 20


x, y ≥ 0


Total profit, Z= 5x + 3y


The mathematical formulation of the given problem is


Maximize Z = 5x + 3y


Subject to constraints


2x + y ≤ 12


And 3x + 2y ≤ 20


x, y ≥ 0


the feasible region determined by the system of constraints can be represented graphically as



The corner points are A( 6,0) , B( 4,4) and C( 0,10)


The value of Z at the corner points are as follows



The maximum value of Z is 32 at B(4,4)


Thus the manufacturer should produce 4 pedestal lamps and 4 wooden shades ti maximize his profits of Rs 32.

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