QUESTION THREE 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.

QUESTION FOUR In a factory, two types of motor are made. Each motor of type 10 man hours to make and each motor of type s 12 man hours to make. In each week there are 200 man hours available. To satisfy customer demand, at least 5 of each type of motor must be made each week. Once a motor has been started it must be completed; no unfinished motors may be left in the factory at the end of each week. When completed, the motors are put into a container for shipping. The volume of the container is 7 3. A occupies a volume of 0.53 and a occupies a volume of 0.33 . a. Define appropriate variables and from the above information derive four inequalities which must be satisfied by those variables. [4 marks] b. Represent your inequalities on a graph and shade the infeasible region. [6 marks] The profit on each type 100 and on each type 70. c. The weekly profit is to be maximized. Write down the objective function and find the maximum profit. [5 marks] d. Because of absenteeism, the manager decides to organize the work in the factory on the assumption that there will be only 180 man hours available each week. Find the number of motors of each type that should now be made in order to maximize the profit. [5 marks]

QUESTION THREE 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.

QUESTION THREE Acompany produces types of party bag. I n die Bohypes of hag contain a balcon a boy and a whistle. In addition, the Inforeg coins 3 sweets and stickers and the enig beg contain 10 weet and stickers. The sto re proceed in the many factory. The factory a produce up to 3000 watts per hour and 1200 sticker per hour. The cr y by a large supply of balloons.oys and whistles Market research indicates that least twice as mer lafant teps as Jusor has show de Bach types of any are sold at a profit of 15p per bag. All the bags are sold The common Wishes to its Let bethember of Infant bar produced and y be the number of Junior approche per la a Fowlane the above Siouxion as a linee programming problem 15 ] Represent your inequalities graphically indicating clearly the feasible region 6 ] c. Find the sur Intesa d i tepi dhe prodach her and the maximum bourly Make your thod clear In order to bury pies the futher, the y decides to buy additional quipment. It can increase the productim of the weet or wicken, um 1. Using your graph, explain which einen should be bought giving your a ing. The manager of the company does not understand why the balloons, toys and whistlesheve been considered in the eakulations Explain willy why they do n ot be consided. 12 marks] QUILSTEIN FOUR la factory, two types are made Bach of type takes 10 r storan wach rotor of type Yakes 12 ansio s rach week there are 3 mon hours available To satisfy ceber demanat least of each type of stor must be made each week. Ocea motor has been stand it must be completo finished motors may be in the factory at the end of each week. When the w in n er for shipping The of the container is 7e A type motor volume of Stew typer occupies a volume of 0. a. Define appr e variables and from the above information dere for inequalities which m be wasted by the variables Represent your inequalities and had the infeasible region 6 mars] The policach type I RI0D and typeY is 70 Wilderne objetive function and find the The kly put isole ma imam pr . d. Because of h i m, the decides to get the work in the factory on the ptice that there will be only 1 Necoch work. Find the number of os of each type that should now be made in order to maximize the politi k QUESTION THREE Acompany produces types of party bag. I n die Bohypes of hag contain a balcon a boy and a whistle. In addition, the Inforeg coins 3 sweets and stickers and the enig beg contain 10 weet and stickers. The sto re proceed in the many factory. The factory a produce up to 3000 watts per hour and 1200 sticker per hour. The cr y by a large supply of balloons.oys and whistles Market research indicates that least twice as mer lafant teps as Jusor has show de Bach types of any are sold at a profit of 15p per bag. All the bags are sold The common Wishes to its Let bethember of Infant bar produced and y be the number of Junior approche per la a Fowlane the above Siouxion as a linee programming problem 15 ] Represent your inequalities graphically indicating clearly the feasible region 6 ] c. Find the sur Intesa d i tepi dhe prodach her and the maximum bourly Make your thod clear In order to bury pies the futher, the y decides to buy additional quipment. It can increase the productim of the weet or wicken, um 1. Using your graph, explain which einen should be bought giving your a ing. The manager of the company does not understand why the balloons, toys and whistlesheve been considered in the eakulations Explain willy why they do n ot be consided. 12 marks] QUILSTEIN FOUR la factory, two types are made Bach of type takes 10 r storan wach rotor of type Yakes 12 ansio s rach week there are 3 mon hours available To satisfy ceber demanat least of each type of stor must be made each week. Ocea motor has been stand it must be completo finished motors may be in the factory at the end of each week. When the w in n er for shipping The of the container is 7e A type motor volume of Stew typer occupies a volume of 0. a. Define appr e variables and from the above information dere for inequalities which m be wasted by the variables Represent your inequalities and had the infeasible region 6 mars] The policach type I RI0D and typeY is 70 Wilderne objetive function and find the The kly put isole ma imam pr . d. Because of h i m, the decides to get the work in the factory on the ptice that there will be only 1 Necoch work. Find the number of os of each type that should now be made in order to maximize the politi k