CBSE Class 12 Mathematics Linear Programming Worksheet Set A

CBSE Class 12 Mathematics Linear Programming Worksheet Set A

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1.A firm manufactures jute bags and cloth bags. The total number of items it can manufacture is at most 24. A Jute bag requires 1 hour to be made while a cloth bag requires only half an hour. The maximum number of hours available per day is 6 hours. If the profit on a jute bag is Rs.30 and on a cloth bag is Rs.20, how many bags of each type must be made for maximum profit? Solve it graphically.

The manufacturer wants to replace cloth bags by plastic bags to increase his profit margin. Is it a good idea? If not, give reasons. Cloth bags are biodegradable while plastic is not. Also cloth bags can be reused.

2. A manufacturer makes cycles and scooters. Processing of these products is done on two machines A and B. The cycle parts need 2 hours on machine A and 6 hours on machine B. Parts of a scooter needs 4 hours on machine A and 2 hours on machine B.

Machine A is available for 16 hours per day and Machine B is available for 30 hours per day. Profit gained by the manufacturers from a cycle and a scooter is Rs.1000 and Rs.3000 respectively. Find with the help of a graph what should be the daily production of each of the two products to maximize the profit? Which of the above modes of transport is a better option and why?

Using cycles is a better option since it is environment friendly and reduces pollution. It is also a good exercise option.

3.There are two types of fertilizers that a farmer uses in his farm namely A and B. A consists of 10 % of nitrogen and 6% phosphoric acid while B contains 5% nitrogen and 10% phosphoric acid. The farmer needs at least 14 kg of nitrogen and 14 kg of phosphoric acid. If A costs Rs. 8/kg and B costs Rs. 6/kg, determine how much of each type of fertilizer should be used by the farmer so that the required nutrient levels are met at minimum cost. What is the minimum cost? The farmer is considering the option of using pesticides to increase his yield. What is your opinion?

Can he convert it into an organic farm? Pesticides may increase the yield but are harmful to mankind. Organic farming is a good option as it is free of use of any chemicals

1. A farmer decides to plant upto 10 hectares with cabbages and potatoes. He decides to grow at least 2 but not more than 8 hectares of cabbages and at least 1 but not more than 6 hectares of potatoes. He can make a profit of Rs. 1500 per hectare on cabbages and Rs.2000 per hectare on potatoes. How should he plan his farming so as to maximize his profit. Keeping in mind the nutritional value of both vegetables, do you think the farmer’s production will help the community? Mention one value point the farmer display?.

Ans: Potatoes are produced more and the farmer’s production will help the community as the potatoes have high protein value than cabbages. So the farmer promotes health awareness .

2 A manufacturer produces two types of disposable plates, one using plastic and the other using bamboo. Three machines are required to produce the plates and the time in minutes is given below.

Each machine is available for a maximum of 6 hours per day. If the profit on each plate of plastic is 75 paise and profit on bamboo plate is 50 paise, how many plates of each type should the factory produce to maximize the profit. Which type of plates do you think should be promoted more and mention one value point as the reason.

Ans: Bamboo plates should be promoted more as they are bio degradable and eco friendly.

3. A principal decides to buy colour boxes and books as prizes for children. A colour box costs Rs.5 and a book costs Rs. 10.He wants to buy at least 4 of each of them. How many of each should he buy so that the expenditure does not exceed Rs.100 and at the same time can give maximum number of prizes? Which of the two , do you think will benefit the children more and mention one value point as the reason.

Ans: Books can benefit more as it promotes reading habit of the children.

Or

Colour Boxes helps to improve their creativity .