Home
Class 12
MATHS
(Manufacturing problem) A manufacturer h...

(Manufacturing problem) A manufacturer has three machines I, II and III installed in his factory. Machines I and II are capable of being operated for at most 12 hours whereas machine III must be operated for atleast 5 hours a day. She produces only two items M and N each requiring the use of all the three machines. The number of hours required for producing 1 unit of each of M and N on the three machines are given in the following table :

She makes a profit of Rs. 600 and Rs. 400 on items M and N respectively. How many of each should she produce so as to maximise her profit assuming that she can sell all the items that she produced? What will be the maximum profit ?

Text Solution

Verified by Experts

The correct Answer is:
Rs. 4000
Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    NCERT GUJARATI|Exercise EXERCISE 12.1 (SOLVE THE FOLLOWING LINEAR PROGRAMMING PROBLEMS GRAPHICALLY:)|6 Videos

  • LINEAR PROGRAMMING

    NCERT GUJARATI|Exercise EXERCISE 12.1 (SHOW THAT THE MINIMUM OF Z OCCURS AT MORE THAN TWO PONTS)|4 Videos

  • LINEAR PROGRAMMING

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE|6 Videos

  • INVERSE TRIGONOMETRIC FUNCTIONS

    NCERT GUJARATI|Exercise MISCELLANEOUS EXERCISE|15 Videos

  • MATRICES

    NCERT GUJARATI|Exercise Miscellaneous Exercise on Chapter 3|15 Videos

Similar Questions

Explore conceptually related problems

Match the column I, II and III

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 Rs. 17.50 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 ?

A manufacturer produces nuts and bolts. It takes 1 hour of worl in machine A and 3 hours on machine B to produce a package of nuts. It take 3 hours on machien A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 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 bis profit, if he operates his machines for at the most 12 hours a day?

A factory owner purchase two types of machines, A and B, for his factory. The requirements and limitations for the machines are as follows : He has an area of 7600 sq.m. available and 72 skilled men who can operate the machines. How many machines of each type should be buy to maximise the daily output ?

A factory owner purchase two types of machines A and B for his factory. The requirements and limitations for the machines are as follows. He has an area of 9000 m^(2) available and 72 skilled persons who can operate the machines. How many machines of each types should he buy to maximise the daily output ?

A small firm manufacturers Golden chains and rings. The total number of chains and rings that it can manufacture in a day is at the most 24. The ring takes 30 minutes. The maximum time available per day is 16 hours. If the profit on the ring be Rs. 300 and one chain be Rs. 190. How many of rings and chains be produced to maximize the profit ?

A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5760 to invest and has space for atmost 20 items. A fan costs him Rs. 360 and a sewing machine Rs. 240. His expectation is that he can sell a fan at pofit of Rs. 22 and a sewing machine at a profit of Rs. 18. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximise his profit ?

The machine used to separate the masive particles and light particles from a mixture is

A manufacturer maks two types A and B of tea cups. Three machines are needed for the manufacture and the time in minutes required for each cup on the machines is given below. Each machine is available for a maximum of 6 hours per day. If the profit on each cup A is 75 paise and that on each cup B is 50 paise. How many both type of tea cups should be manufactured in a day to get the maximum profit ?

(Manufacturing problem) A manufacturing company makes two models A and B of product. Each piece of Model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of Model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs. 8000 on each piece of model A and Rs. 12000 on each piece of Model B. How many pieces of model A and model B should be manufactured per week to realise a maximum profit ? What is the maximum profit per week ?