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QUESTION 1 |2(I marks| The Luxury produces two sizes of trolley bags regular and large. The trolley,' bags are produced in 10,000 lots. The uolley bags are processed through a sewing operation and an assembling operation. The company has 30 days available for both sewing and assembling. A lot of regular-size trolley bag requires 2 days to sew and 4 days to assemble, Whereas a lot of large Holley bag requires 4 days to sew and 2 days to assemble. A lot of regular-size trolley bag earns $300, and a lot of large-size trolley bag earns $900 prot. In order to lll its obligations under a shipping contact, the company could produce at most nine lots. The company wants to determine the number of lots to produce regular and large size trolley bags (X1 and X2 respectively} in order to maximize prot. a) Formulate the above probl- as a linear programming model. [5 marks] b) Set up an initial simplex table for the above linear programming model. ' [5 marks] Answer the following questions based on the nal simplex tableau given below: mnmnnn _ MU\" -nm MIX mun-nun\" -i-_-_-i---_\" _\"_M\" -m_m- _---s--_-n-m- where X1 = Output of regular trolley bags; X2 = Output of large trolley bags 31 = Slack for sewing; 32 = Slack for assembling; 33 = lots c) State the optimum output mix and the associated maximum prot. [4 marks] d) Assuming that there are three resources at this stage, what are the resources that are fully utiliZed and which resource is still not fully utilized? [3 marks] e) If the premium required for one additional sewing operation is RMO per day, is it worth acquiring additional units of this resource? Explain your answer. [3 marks]