A firm operates two types of machines A and B as shown in the table. Type A Type B 3 2 5 3 Floor Space Available (M²) Number of Workers Maximum Space Available 18 30 The ratio of machines of type A to those of type B should be greater than one. Tasks a) Define the term linear programming | b) Write down four inequalities to represent the information above c) If the profit from using type A machine is Shs 6000 per hour and that of B is Shs 9000 per hour, write down the expression for the profit P in terms of x and y d) Find the number of machines of each type that should be in operation to give the maximum profit. Hence find the maximum profit e) What advice do you give to this company's manager

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