Please solve 11.1

Problem#1 Formulate a linear programming model for problem 11.1 of the below image and find its optimal solution using a graphical method. PROBLEMS Cost per Type of Number of flars Number Plan block in category of storeys area block 1 2 3 4 (Smillion) 0 113 5 11.4 Two additives, X1 and X2, can be used to increase the octane number of petrol. 1 kilogram of X1 in 5,000 litres of petrol Increases the octane number by 10, while 1 kilogram of X2 in 5,000 litres increases the octane number by 20. The total additives must increase the octane number by at least 5, but a total of no more than 500 grams can be added to 5,000 litres, and the amount of x2 plus twice the amount of Xi must be at least 500 grams. of X1 costs 30 a kilogram and X2 costs 40 a kilogram, formulate this problem as a linear programme. Use a graphical method to find an optimal solution. B d D E 2.08 3.2 3.0 48 4.8 88 6 4 OO 10 The association wants to build a total of 500 flats with at least 40 in category 1 and 125 in each of the other categories. In the past, high-rise flats have proved unpopular and the association wants to limit the number of storeys In the development - with the average number of storeys at most five, and at least half the flats in blocks of three or fewer storeys. An area of 300 units has been set aside for the development and any spare land will be used as a park. Formulate this problem as a linear programme 11.2 North Penberthy Housing Association is planning a number of blocks of flats. Five types of block have been designed, containing flats of four categories (1 - senior citizens, 2 - single person, 3 - small family and 4-large family). The number of flats in each block, and other relevant information, is as follows: Jir nc ba we