A company produces two types of party bag, Infant and Junior. Both types of bag contain a balloon, a toy and a whistle. In addition, the Infant bag contains 3 sweets and 3 stickers and the Junior bag contains 10 sweets and 2 stickers. The sweets and stickers are produced in the companys factory. The factory can produce up to 3000 sweets per hour and 1200 stickers per hour. The company buys a large supply of balloons, toys and whistles. Market research indicates that at least twice as many Infant bags as Junior bags should be produced. Both types of party bag are sold at a profit of 15p per bag. All the bags are sold. The company wishes to maximize its profit. Let x be the number of Infant bags produced and y be the number of Junior bags produced per hour. a. Formulate the above situation as a linear programming problem. [5 marks] b. Represent your inequalities graphically, indicating clearly the feasible region. [6 marks] c. Find the number of Infant bags and Junior bags that should be produced each hour and the maximum hourly profit. Make your method clear. [4 marks] In order to increase the profit further, the company decides to buy additional equipment. It can buy equipment to increase the production of either sweets or stickers, but not both. d. Using your graph, explain which equipment should be bought, giving your reasoning. [3 marks] The manager of the company does not understand why the balloons, toys and whistles have not been considered in the above calculations. e. Explain briefly why they do not need to be considered. [2 marks]