# A cottage industr

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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