Answer :

let the number of packages of nuts produce be x

Let the number of bolts produced be y

The tabular representation of data given is as follows:

The system of constraints is given as

x + 3y ≤ 12

& 3y + x ≤ 12

Where x and y ≥ 0

We need to maximize the profit, so the function here will be maximizing Z

Maximize Z = 17.5x+ 7.5y

Subject to constraints

x + 3y ≤ 12

& 3y + x ≤ 12

Where x and y ≥ 0

The corner points are A(4 , 0) , B( 3,3) , C( 0 , 4) and O( 12, 0)

Hence the profit will be maximum if the company produces

Number of bolts – 3 packages

Number of nuts – 3 packages

Maximum profit is Rs 73.50

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