# CBSE Class 12-science Maths Optimal Solution

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- A company manufactures two articles A and B. There are two departments I and II through which these articles are processed. The maximum capacity of department I is 60 hours a week and that of department II is 48 hours a week. The production of each article A requires 4 hours by department I and 2 hours by department II and that of each unit of B requires 2 hours in department I and 4 hours in department II. If the profit of Rs 60 for each unit of A Rs 80 for each unit of B find the number of units of A and B to be produced per week to have maximum profit.
- A diet is to contain atleast 10 units of vitamin A, 12 units of vitamin B and 8 units of calcium. Two foods f
_{1}and f_{2}are available. A unit of food f_{1}contains 1 unit of vitamin A, 2 units of vitamin B and 3 units of calcium and a unit of food f_{2}contains 2 units of vitamin A, 2 units of vitamin B and 1 unit of calcium. If one unit of food f_{1}costs Rs 16 and one unit of food f_{2}costs Rs 20, find the least cost of the mixture which will produce the desired diet. - One kind of cake requires 200 g of flour and 25 g of fat and another kind of cake requires 100 g of flour and 50 g of fat find the maximum number of cakes which can be made from 5 kg of flour and 1 kg of fat assuming that there is no shortage of other ingredients, used in making cakes.
- A dealer deals in two items decorative plant and lamp shade. He has 10000 to invest and a space to store atmost 60 pieces. A decorative plant costs him Rs 500 and lamp shade costs him Rs 100. He can sell a decorative plant at Rs 550 and a lamp shade at Rs 115. Assuming he can sell all the items, find his maximum profit.
- A manufacturer makes Rs 600 profit on stereo system and Rs 400 profit on small tape recorder. A stereo requires 1 hour on machine A, 1 hour on machine B and 4 hours on machine C. A tape recorder requires 2 hours on A, 1 hour on B and 1 hour on C. In a given day, machines A, B and C can working a maximum of 16, 9 and 24 hours respectively. How many stereo systems and tape recorders should be produced per day to maximize the profit.
- A calculator company produces a scientific calculator and a standard calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 standard calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 standard calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If each scientific calculator sold results in a Rs 2 loss, but each standard calculator produces a Rs 5 profit, how many of each type should be made daily to maximize net profits?
- In order to ensure optimal health (and thus accurate test results), a lab technician needs to the dogs a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the dog should be fed no more than five kg of food a day. Rather than to order dog-food that is custom-blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per kg, and costs Rs0.20 per kg. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per kg, at a cost of Rs0.30 per kg. What is the optimal blend?
- A dealer wishes to purchase a number of fans and sewing machines. He has only Rs. 5760.00 to invest and has space for at most 20 items. A fan costs him Rs.360.00 and a sewing machine Rs. 240.00. His expectation is that he can sell a fan at a profit of Rs. 22.00 and sewing machine at a profit of Rs. 80.00. Assuming that he can sell all the items that he can buy, how should he invest his money in order to maximize his profit? Translate this problem mathematically and then solve it.
- A shopkeeper wants to sell T.V.and Refrigerators.A Refrigerator costs him 20000 Rs and a T.V. costs him 10000 Rs. He has 300000 Rs to invest.To maintain his dealership he must sell at least 3 Refrigerators and he can sell atmost 9 T.V. he has 24 sq unit of area to accommodate them. If a refrigerator requires 1 squnit and a T.V. requires 2 sq unit , find how many units of eachshould be kept so as to maximize the profit.
- <div>The letters of the word 'SURITI ' are written in all possible order and these words are written out as in a dictionary. Find the rank of the word 'SURITI '?</div>

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