A person requires at least 10,12 and 12 units of chemicals A ,B and C respectively for his garden. A liquid product contains 5,2 and 1 units of A,B and C respectively per jar. A dry product contains 1,2 and 4 units of A,B and C per carton. Formulate the given data in the form of inequations and show graphically the region representing the solution of these inequations.

A diet is to contain at least 400 units of carbohydrate, 500 units of fat and 300 units of protein. Foods F_1 contains 10 units of carbohydrate, 20 units of fat and 15 units of protein and food F_2 contains 25 units of carbohydrate,10 units of fat and 20 units of protein. Formulate the given data in the form of inequations and show graphically the region representing the solution of these inequations.

A manufacturer produces two types of articles A and B. The production cost of an article A is Rs.250 and that of B is Rs.300. His total investment does not exceed Rs.20000 and he can store at most 100 articles. Formulate tha given data in the form of inequations and show graphically the region representing the solution of these inequations.

A pharmaceutical company requires everyday 10,12,12 units of chemicals C_1,C_2 and C_3 respectively. A liquid product contains 5,2,and 1 units of chemicals C_1, C_2 and C_3 respectively per bottle and its cost is Rs.300 per bottle. A dry product contains 1,2 and 4 units of chemicals C_1, C_2 and C_3 respectively per box and it costs Rs.200 per box. how much quantitiy of either of the two products should be purchased daily in order to minimize the cost.

A man has to spend Rs.16 per km on petrol if he rides his motor-car at 30 km per hour and the cost on petrol rises to Rs.20 per km if he rides his car at 45 km per hour. He has Rs.200 to spend on petrol and desires to travel maximum distance within 2 hours. Formulate the given data in the form of inequations and show graphically the region representing the solution of the inequations.

A factory uses three different resources for the manufacture of two different productoof the resource A, 12 units of B and 16 unit of C being available. One unit of there quires 2, 2 and 4 units of the respective resources and one unit of the second requires 4,2 and 0 units of respective resources. It is known that the first product givesatof 2 monetary units per unit and the second 3. Formulate the linear programming problem How many units of each product should be manufactured for maximizing the profit? solve it graphically.

A farm is engaged in breeding hens. The hens are fed products A and B grown in the farm which contains nutrients P, Q and R. One kilogram of product A contains 36 units, 3 units and 20 units of nutrients P Q and R respectively, whereas one kilogram of product B contains 6 units, 12 units and 10 units of nutrients P, Q and R respectively. The minimum requirement of nutrients P Q and R for a hen is 108, 36 and 100 units respectively. Product A costs 20 per kilogram and product B costs 40 per kilogram. Using linear programming, find the number of kilograms of products A and B to be produced to minimize the total cost. Identify the feasible region from the rough sketch.

K_c for A + B ⇌ C + D is 10 at 25^o C . If a container contains 1,2,3,4 mole per litre of A,B,C, and D respectively at 25^o C , the reaction shall :

A diet is to contain at least 80 units of Vitamin A and 100 units of minerals. Two foods F1 and F2 are available. Food F1 costs Rs. 4 per unit and F2 costs Rs. 6 per unit. One unit of food F1 contains 3 units of Vitamin A and 4 units of minerals. One unit of food F2 contains 6 units of Vitamin A and 3 units of minerals. Formulate this as a linear programming problem and find graphically the minimum cost for diet that consists of mixture of these two foods and also meets the minimal nutritional requirements.