using SIMPLEX METHOD, solve the following linear programming problems

A farmer has 5 hectares of land to plant with rice and corn. He needs to decide how many hectares of rice and corn to plant. He can make P200,000 profit per hectare planted to rice and P250,000 profit per hectare planted with corn. However, the corn takes 2 hours of labor per hectare to harvest, and the rice takes 1 hour per hectare. The farmer has 8 hours of labor to harvest. To maximize his profit, how many hectares of each should he plant?Rabbits in the laboratories used for drug testing have to be fed a daily diet for accurate results. The diet must contain a minimum of 24 grams of fat, 36 grams of carbohydrates and 4 grams of proteins. The rabbits should be fed not more than five ounces of food per day. A laboratory technician blends food X and food Y to produce an optimal mixture. Food X contains 8 grams of fat, 12 grams of carbohydrates and 2 grams of protein per ounce and costs P200 per ounce. Food Y contains 12 grams of fat, 12 grams of carbohydrates and 1 gram of protein per ounce at a cost of P300 per ounce. What is the optimal blend to minimize the cost?Rabbits in the laboratories used for drug testing have to be fed a daily diet for accurate results. The diet must contain a minimum of 24 grams of fat, 36 grams of carbohydrates and 4 grams of proteins. The rabbits should be fed not more than five ounces of food per day. A laboratory technician blends food X and food Y to produce an optimal mixture. Food X contains 8 grams of fat, 12 grams of carbohydrates and 2 grams of protein per ounce and costs P200 per ounce. Food Y contains 12 grams of fat, 12 grams of carbohydrates and 1 gram of protein per ounce at a cost of P300 per ounce. What is the optimal blend to minimize the cost?A hog raiser is mixing two types of grains A and B. Each unit of grain A costs P50 and contains 20 grams of fat and 10 grams of protein. Each unit of grain B costs P80 and contains 30 grams of fat and 30 grams of proteins. The hog raiser wants each unit of the final product to yield at least 180 grams of fat and at least 120 grams of protein. How many units of each type of grain should he use to maximize his sales