Q7 of 17 Page 12

A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs17.50 per package on nuts and Rs 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day?[CBSE 2012]

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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A cottage industry manufactures pedestal lamps and wooden shades, each requiring the use of a grinding/cutting machine and a sprayer. It takes 2 hours on grinding/cutting machine and 3 hours on the sprayer to manufacture a pedestal lamp. It takes 1 hour on the grinding/cutting machine and 2 hours on the sprayer to manufacture a shade. On any day, the sprayer is available for at the most 20 hours and the grinding/cutting machine for at the most 12 hours. The profit from the sale of a lamp is Rs 5 and that from a shade is Rs 3. Assuming that the manufacturer can sell all the lamps and shades that he produces, how should he schedule his daily production in order to maximise his profit?[CBSE 2014]