Question 6: Linear Programming The Morpeth Sauce Company has two best selling products, a Barbecue Sauce and a Relish. The company must make at least 6 batches of Relish each week to meet a standing customer order. Each batch of Barbecue Sauce requires 15 kg of Onions as a key raw ingredient and each batch of Relish requires 10 kg of Onions. The company can obtain a maximum of 480 kg of Onions available each week. The Barbecue Sauce and Relish are packed into jars for sale. There are 160 hours of labour available each week for packing. Each batch of Barbecue Sauce requires 2 hours of labour to pack. Each batch of Relish requires 4 hours of labour to pack. a) Use the above information to write down the three inequalities relating to the resource requirements when producing Relish and Barbecue Sauce. Remember to define your variables clearly. [4 marks] b) The Relish has a profit of 380 per batch and the Barbecue Sauce has a profit of 400 per batch. Determine how many batches of Relish and Barbecue Sauce the company should produce each week to maximise their profits. (sketching the graph will help to identify the feasible points however the graph does not need to be shown in your final answer). [4 marks] b) The Relish has a profit of 380 per batch and the Barbecue Sauce has a profit of 400 per batch. Determine how many batches of Relish and Barbecue Sauce the company should produce each week to maximise their profits. (sketching the graph will help to identify the feasible points however the graph does not need to be shown in your final answer). (4 marks] c) Calculate the shadow price for increasing the Onions resource [4 marks] d) Write a brief interpretation of the shadow price calculated in part c) [2 marks] 12pt Paragraph