a) A simple economy has a manufacturing industry and a banking industry. Each unit of manufacturing output requires inputs of 0.3 unit of manufacturing and 0.6 unit of banking. Each unit of banking industry output requires inputs of 0.2 unit of manufacturing and 0.2 unit of banking. i. If surpluses of 641 units of manufacturing and 10 units of banking are desired, find the gross production to the nearest unit of each industry. ii. (7 marks) Find the additional production needed from each industry for 7 more unit of banking surplus. (3 marks) b) A farm in Kedah has 6000 acres available to plant with rubber tree and oil palms. Each 3 acre of rubber trees requires 9 gallons of fertilizer/herbicide and hour of labor to 4 harvest. Each acre of oil palms requires 3 gallons of fertilizer/herbicide and 1 hour of labor to harvest. The farm has available at most 40,500 gallons of fertilizer/herbicide and at most 5250 hours of labor for harvesting. The profits per acre are RM60 for rubber tree and RM40 for oil palms. The number of acres of each crop is constrained by the available resources: land, fertilizer/herbicide, and labor for harvesting. i. Write the inequalities that describe the constraints on the number of acres each crop produced. (3 marks) ii. Graph the inequalities in part (i) and shade the feasible region determined by these constraints. (5 marks) iii. Find how many numbers of acres of rubber tree and oil palms that the farm could plant to maximize profit. iv. Find the maximum profit (5 marks) (2 marks)