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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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