Class 12 CBSE Applied Maths Linear Programming Exercise 15.3

Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their applications in the field of commerce (business/ finance/economics) and social sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.


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Exercise 15.1 Exercise 15.2 Case Study

Q1. A company manufactures two types of screws A and B. All the screws have to pass through a threading machine and a slotting machine. A box of type A screws requires 2 minutes on threading machine and 3 minutes on slotting machine. A box of type B screws requires 8 minutes on threading machine and 2 minutes on slotting machine. In a week, each machine is available for 60 hours. On selling these screws, the company gets a profit of Rs 100 per box on type A screws and Rs 170 per box on type B screws. How many boxes of screws of each type should be manufactured to get maximum profit. Form it as an L.P.P. and solve graphically using iso- profit/iso-cost method.

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Q2. A manufacturer produces two models of bikes-model X and model Y. Model X takes a 6 man-hours to make per unit, while model Y takes 10 man-hours per unit. There is a total of 450 man-hours available per week. Handling and marketing costs are ₹2000 and ₹1000 per unit for Models X and Y respectively. The total funds available for these purposes are ₹80000 per week. Profit per unit for models X and Y are ₹1000 and ₹600 respectively. How many bikes of each model should the manufacturer produce so as to yield a maximum profit? Form an L.P.P. and solve it graphically using iso-profit/iso-cost method.

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Q3. Suppose every gram of wheat provides 0.1 g of proteins and 0.25 g of carbohydrates, and the corresponding values for rice are 0.05 g and 0.5 g respectively. Wheat costs ₹20 and rice ₹30 per kilogram. The minimum daily requirement of an average man for proteins and carbohydrates is 50 g and 200 g respectively. Find what quantities of wheat and rice be mixed in the daily diet to provide the minimum daily requirements of proteins and carbohydrates at minimum cost and also find the minimum cost? Form an L.P.P. and solve it graphically using iso-profit/iso-cost method.

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Q4. To maintain one's health, a person must fulfil certain minimum daily requirements for the following three nutrients - calcium, protein and calories. His diet consists of only food items I and II whose prices and nutrient contents are shown below:

Find the combination of food items so that the cost may be minimum. Form an L.P.P. and solve it graphically using iso-profit/iso-cost method.

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