TD Sdn Bhd is one of the largest manufacturers of furniture in Malaysia. The types of furniture being manufactured include chair, bench, and table, in which the manufacturing process involves two departments namely the tube-bending department as well as the welding department. The time required to manufacture each product in each department is depicted in the following table: Types of Furniture Maximum capacity Chair Bench Table Tube bending (hours) 1.8 2.5 1.5 1,100 Welding (hours) 1.1 0.3 3.4 1,300 The sale of a unit of chair earns TD Sdn Bhd a contribution of RM2.70, RM3.30 for a bench, and RM5.30 for a table. The firm is apparently planning its production mix for the Grand Sale event and it aims to maximize contribution. It is estimated that it can sell any number it manufactures. However, production is further limited by the availability of raw material. Apparently, the firm possesses 2,500 lbs. of metal tubing. The manufacturing process of the furniture requires the following amounts of this metal tubing: 2.5 lbs. per chair, 3.1 lbs. per bench, and 4.7 lbs. per table. Candidates are to formulate and to solve this problem approximately using continuous variables and round down to the nearest discrete value upon the finding of solution. (a) Formulate the linear programming model according to the above problem. (7 marks) (b) Identify the optimal combination of production and the anticipated contribution by manufacturing based on the combination. Solve the problem using Excel Solver. (6 marks) (c) What is the shadow price of tube-bending time, welding time and metal tubing? (3 marks) (d) Identify the slack and surplus variables. (3 marks) (e) Answer the following questions based on the Excel spreadsheet output: (i) The supplier of raw material has offered TD Sdn Bhd to buy some additional metal tubing for RM0.80/lb. Should TD Sdn Bhd purchase it? Justify your answer. (3 marks) (ii) If TD Sdn Bhd. raises extra 2 hours of tube bending time, estimate its maximum contribution by using shadow variable. Should the firm add these additional 2 hours of tube bending time? Justify. (Show your calculation and answer). (7 marks) (iii) If TD Sdn Bhd decreased 3 hours of welding time, estimate its maximum contribution by using shadow variable. Should the firm decrease the welding time? Justify. (Show your calculation and answer). (7 marks) (iv) Assuming that the contribution of bench has risen from RM3.30 to RM5.20. Calculate the new contribution. (4 marks) [