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1. A tailoring business makes two types of garments A and B. Garment A requires 3 metres of material while garment B requires 2 12 metres of material. The business uses not more than 600 metres of material daily in making both garments. It must make not more than 100 garments of type A and not less than 80 of type B each day. (a) Write down four inequalities from this information. (3mks) (b) Graph these inequalities. (3mks) (c) If the business makes a profit of shs 80 on garment A and a profit of shs 60 on garment B. how many garments of each type must it make in order to maximize the total profit? (4mks) 2. A man bakes two types of cakes, queen cakes and marble cakes. Each week he bakes x queen cakes and y marble cakes. The number of cakes baked are subject to the following conditions; 30x + 20y s 4800, 30x + 40y > 3600 and 10x >30y He makes a profit of shs. 10 on each queen cake and shs.12 on each marble cake. (i) Draw a graph to represent the above information on the grid provided (ii) From the graph, determine how many cakes of each type he should make to maximize his weekly profit (iii) Calculate the maximum profit (iv) If he is to make a weekly profit of at least shs.600, find the least number of marble cakes he should bake 3. A company produces shirts and jerseys using two types of machines. Every shirt made requires 2 hours on machine A and 2 hours on machine B. Every Jersey made requires 3hours on machine A and I hour on machine B. In one day the time limit on machine A is 24hours but that on machine B is 12hrs. The number of Jerseys produced must not be more than the shirts produced in one day. The company makes a profit of shs.200 on each shirt and shs.200 on each Jersey. The company produces x shirts and y jerseys per day (a) Write down four inequalities which must be satisfied by x and y and represent these inequalities on a grid (b) Find the values of x and y which will give the company maximum daily profit and also state the maximum profit 4. A trader makes two types of chair, ordinary and special chairs. The cost of each ordinary chair is shs.300 while each special chair costs shs. 700. He is prepared to spend not more than shs.21,000. It is not viable for him to make less than 20 chairs. Ordinary chairs must be less than twice the special chairs but more than 15. By taking the number of ordinary chairs as x and special chairs as y: (a) Write down all the inequalities in x and y (b) Draw the inequalities on the grid provided (c) He sells a special chair at a profit of shs. 140 while ordinary chairs at a profit of shs. 120; Determine the maximum possible profit1. A tailoring business makes two types of garments A and B. Garment A requires 3 metres of material while garment B requires 2 12 metres of material. The business uses not more than 600 metres of material daily in making both garments. It must make not more than 100 garments of type A and not less than 80 of type B each day. (a) Write down four inequalities from this information. (3mks) (b) Graph these inequalities. (3mks) (c) If the business makes a profit of shs 80 on garment A and a profit of shs 60 on garment B, how many garments of each type must it make in order to maximize the total profit? (4mks) 2. A man bakes two types of cakes, queen cakes and marble cakes. Each week he bakes x queen cakes and y marble cakes. The number of cakes baked are subject to the following conditions; 30x + 20y = 4800, 30x + 40y a 3600 and 10x >30y He makes a profit of shs. 10 on each queen cake and shs. 12 on each marble cake. (i) Draw a graph to represent the above information on the grid provided (ii) From the graph, determine how many cakes of each type he should make to maximize his weekly profit (iii) Calculate the maximum profit (iv) If he is to make a weekly profit of at least shs.600, find the least number of marble cakes he should bake 3. A company produces shirts and jerseys using two types of machines. Every shirt made requires 2 hours on machine A and 2 hours on machine B. Every Jersey made requires 3hours on machine A and I hour on machine B. In one day the time limit on machine A is 24hours but that on machine B is 12hrs. The number of Jerseys produced must not be more than the shirts produced in one day. The company makes a profit of shs.200 on each shirt and shs.200 on each Jersey. The company produces x shirts and y jerseys per day (a) Write down four inequalities which must be satisfied by x and y and represent these inequalities on a grid (b) Find the values of x and y which will give the company maximum daily profit and also state the maximum profit A trader makes two types of chair, ordinary and special chairs. The cost of each ordinary chair is shs.300 while each special chair costs shs. 700. He is prepared to spend not more than shs.21,000. It is not viable for him to make less than 20 chairs. Ordinary chairs must be less than twice the special chairs but more than 15. By taking the number of ordinary chairs as x and special chairs as y: (a) Write down all the inequalities in x and y (b) Draw the inequalities on the grid provided (c) He sells a special chair at a profit of shs. 140 while ordinary chairs at a profit of shs. 120; Determine the maximum possible profit
