A company uses linear programming to establish an optimal production plan in order to maximise profit. The company finds that for the next year materials and labour are likely to be in short supply. tails of the company's products are as follows Product A Materials (@N$2 per kg) Labour (@NS6 per hour) Variable overheads (ON$1 per hour) N$ 6 30 Product EB N$ 8 18 3 The selling price for product A is N$50 and product B is N$52 per unit respectively There are only 30 000 kg of material and 36 000 labour hours available. The company also has an agreement to supply 1 000 units of product A which must be met. Requirement Marks Use the graphical method with simultaneous equation and determine the11 combination of product A and product B to be made to make optimum profits, determining the profit at each extreme point in the feasible region Calculate the value of any slack and surplus and explain what they mean using your answer in (a) above. a) b) c) Explain how this company could use shadow prices Total marks 4 18 Page 8 of 11 A company uses linear programming to establish an optimal production plan in order to maximise profit. The company finds that for the next year materials and labour are likely to be in short supply. tails of the company's products are as follows Product A Materials (@N$2 per kg) Labour (@NS6 per hour) Variable overheads (ON$1 per hour) N$ 6 30 Product EB N$ 8 18 3 The selling price for product A is N$50 and product B is N$52 per unit respectively There are only 30 000 kg of material and 36 000 labour hours available. The company also has an agreement to supply 1 000 units of product A which must be met. Requirement Marks Use the graphical method with simultaneous equation and determine the11 combination of product A and product B to be made to make optimum profits, determining the profit at each extreme point in the feasible region Calculate the value of any slack and surplus and explain what they mean using your answer in (a) above. a) b) c) Explain how this company could use shadow prices Total marks 4 18 Page 8 of 11