The prices of three commodities A,B and C are Rs x, y and z per unit respectively. A person P purchases 4 units of B and sells two units of A and 5 units of C. Person Q purchases 2 units of C and sells 3 units of A and one unit of B. Person R purchases one unit of A and sells 3 unit of B and one unit of C. In the process, PQ and R earn Rs 15,000, Rs 1,000 and Rs 4,000 respectively. Find the prices per unit of A,B and C. (Use matrix inversion method to solve the problem.)

The prices of three commodities P ,\ Q ,\ a n d\ R are Rs x ,\ y\ a n d\ z per unit respectively. A purchases 4 units of R and sells 3 unit of P and 5 units of Qdot B purchases 3 units of Q and sells 2 units of P and 1 unit of Rdot C purchases 1 unit of P and sells 4 units of Q and 6 units of Rdot In the process A ,\ B\ a n d\ C earn Rs 6000, 5000 and 13000 respectively. If selling the units is positive earning and buying the units is negative earnings, find the price per unit of three commodities by using matrix method.

A consumer purchased 10 units of a commodity when its price was ₹ 5 per unit. He purchased 12 units of the commodity when its price fell to ₹ 4 per unit. What is the price elasticity of demand for the commodity ?

A diet for a sick person must contain atleast 4000 units of vitamin, 50 units of minerals and 1400 units of calories. Two foods A and B are available at a cost of Rs.5 and Rs.4 per unit respectively. One unit of food A contains 200 units of vitamin, 1 unit of minerals and 40 units of calories, while one unit of food B contains 100 units of vitamins, 2 units of minerals and 40 units of calories. find what combination of food A and B should be used to have least cost, but it must satisfy the requirements of the sick person? form the question as an LPP and solve it graphically.

A company manufactures two types of chemicals A and B. Each chemical requires the types of raw materials P and Q. The table below shows number of units of P and Q required to manufacture one unit of A and one unit of B and the total availability of P and Q. The company gets profit of Rs. 350 and RS.400 by selling one unit of A and one unit of B respectively. If the entire production of A and B is sold, then formulate the problem as LPP.

A producer has 30 and 17 units of labour and capital respectively which he can use to produce two of goods X and Y. To produce one unit X, 2 units of labour and 3 units of capital are required. Similarly, 3 units of labour and 1 unit of capital is required to produce one unit of Y. If X and Y are priced at Rs. 100 and Rs. 120 per unit respectively to should be producer use his resources to maximize the total revenue?