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# 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]**

**[CBSE 2012]**

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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PREVIOUSA factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.
(i) What number of rackets and bats must be made if the factory is to work at full capacity?
(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity. [CBSE 2011]NEXTIf a young man drives his scooter at a speed of 25 km/hr, he has to spend Rs2 per km on petrol. If he drives the scooter at a speed of 40 km/hour, it produces air pollution and increases his expenditure on petrol to Rs 5 per km. He has a maximum of Rs100 to spend on petrol and travel a maximum distance in one hour time with less pollution. Express this problem as an LPP and solve it graphically. What value do you find here?[CBSE 2013]

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