Question Three: Linear Programming [15 Marks] A company makes a product in two different factories. At factory X it takes 30 hours to produce the product and at factory Y it takes 20 hours. The costs of producing these items are R50 at factory X and R60 at factory Y. The company's labour force can provide 6000 hours of labour each week and resources are R12 000 each week. Management has decided that at least 100 units must be made in each factory. How should the company allocate its labour and resources to maximize the number of products produced? (Hint: Remember to clearly have your objective function, constraints, coordinates, graph and your possible profits at the feasible points. Also remember to actually answer the question.)