• Use the principles of linear programming to maximize or minimize and interpret the following situation.
• Impact Printing manufactures two types of computer paper using either premium or ordinary quality paper. They have a contract to supply at least 5,000 boxes of paper. There is only enough stock to make 4,000 boxes of premium paper, but there is ample stock for plain paper. Both types are made on the same machine and 1200 hours of machine time are available. Premium paper takes 18 minutes per box to make and plain paper takes 12 minutes per box. The profit for each is $4/box and $3/box, respectively. Use the principles of linear programming to find the optimal solution.

• A dietitian wishes to mix two types of food in such a way that the vitamin content of the mixture contains at least 8 units of vitamin A and 10 units of vitamin C. Food 'I' contains 2 units/kg of vitamin A and 1 unit/kg of vitamin C. Feed 'II' contains 1 unit/kg of vitamin A and 2 units/kg of vitamin C. It costs Rs 50 per kg to buy feed 'I' and Rs 70 per kg to buy feed ' me''. Use the principles of linear programming to minimize the cost of mixing.

• A cooperative society of farmers has 50 hectares of land for two crops, X and Y. Earnings for crops X and Y per hectare are estimated at Rs 10,500 and Rs 9,000, respectively. To control weeds, a liquid herbicide should be used for crops X and Y at a rate of 20 liters and 10 liters per hectare. Also, to protect fish and wildlife no more than 800 liters of herbicide should be used and a pond that collects drainage from this land is recommended. Use the principles of linear programming to determine what land should be allocated to each crop in order to maximize the total benefit to society.