A factory produces product X and product Y. Product X needs 30 minutes of labour time, while product Y needs 15 minutes. The materials needed for each product X and each product Y are 2.5 kilograms and 2 kilograms respectively. The testing process for product X is 3 minutes, while for product Y is 4 minutes. In any one week, only 60 hours of labour time are allocated and 500 kilograms of materials are available. Owing to cost and availability, the testing equipment must be used at least 8 hours. Due to existing orders, at least 40 units of product X and 80 units of product Y must be produced. The profits from each unit of X and Y produced are RM 6.00 and RM 4.50 respectively. If x is the number of units of product X and y is the number of units of product Y produced, (a) Determine and draw the objective function to maximize the profit and formulate the given information in a form of linear programming model. [6 marks] (b) by using graph paper, shade the feasible region satisfying the system of inequalities in part (a). [5 marks] (c) find the weekly production for each product that will maximize the profit and state the expected maximum profit. [4 marks]