A factory produces three items P,Q and R at two plants A and B . The number of items produced and operating costs per hour is as follows:
It is desired to produce at least 500 items of type P , at least 400 items of type Q and 300 items of type R per day.
Is it a maximisation case or a minimisation case? Why?

A factory produces three items P,Q and R at two plants A and B . The number of items produced and operating costs per hour is as follows: It is desired to produce at least 500 items of type P , at least 400 items of type Q and 300 items of type R per day. Write the objective function and constraints.

(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 where as 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 item should she produce so as to maximise her profit assuming that she can swll all the items that she produced ? What will be the maximum profit ?

A manufacturer has three machine operators A,B and C. The first operator A produces 1% defective items,whereas the other two operator B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time,B is on the job 30 % of the time and C is on the job for 20% of the time. A defective item is produced,what is the probability that it was produced by A?

A factory manufactures two types of screws, A and B . Each type of screw requires the two machines, an automatic and a hand operated.It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screw A at a profit of Rs 7 and screws B at a profit of Rs 10 . Assuming that he can sell all the screws he manufactures, how many packages of eách type should the factory owner produce in a day in order to maximise his profit? Determine the maximum profit.

In factory there are two machines A and B producing toys.They respectively produce 60 and 80 units in one hour.A can run a maximum of 10 hours and B a maximum of 7 hours a day .The cost of their running per hour respectively amount to 2,000 and 2,500 rupee.The total duration of working these machines cannot exceed 12 hours a day.If the total cost cannot exceed Rs. 25,000 per day and the total daily production is atleast 800 units,then formulate the problem mathematically.

A man owns a field of area 1,000 sq.m. He wants to plant fruit trees in it. He has a sum of Rs. 1,400 to purchase young trees. He has the choice of two types of the tree. Type A requires 10 sq.m of ground per tree and cost. Rs. 20 per tree and type B requires 20 sq.m of ground per tree and cost Rs. 25 per tree. When fully grown, type A produces an average of 20 kg fruit Which can be sold at a profit of Rs. 2 per kg and type B produces. an average of 40 kg of fruit which can be sold at a profit.of Rs. 1.50 per kg. How many of each type should he plant to achieve maximum profit when the trees are fully grown? What is the maximum profit?

A firm manufactures two types of products A and B and sells them at a profit of Rs. 5 per unit of type A and Rs. 3 per unit of type B . Each product is processed on two machines M_1 and M_2 . One unit of type A requires one minute of processing time, on, M_1 and two minutes of processing time on M_2 whereas one unit of type B requires one minute of processing time on M_1 and one minute of M_2 . Machines M_1 and M_2 are respectively available for at most 5 hours and 6 hours a day. Find how many, units of each type of product should the firm produce a day, in order, to maximise the profit. Solve thè problem graphically.

A manufacturer makes two types of tea cups, say A and B. Three machines are needed for the manufacturing and the time in minutes required for each cup on the machine is given below: Each machine is available for a maximum of 6 hrs per day. If the profit on each cup A is 75 paise and that on each cup B is 50 paise. If x and y denote the number of cups of ttpe A and B produced in a day respectively. What are the linear in equations satisfied by x and y ?

A manufacturer makes two types of tea cups, say A and B. Three machines are needed for the manufacturing and the time in minutes required for each cup on the machine is given below: Each machine is available for a maximum of 6 hrs per day. If the profit on each cup A is 75 paise and that on each cup B is 50 paise. If x and y denote the number of cups of ttpe A and B produced in a day respectively. What is the profit function ?