... Answer question 1 to 7. No handwritten answers please

11:01 PMMI'i (a i1l..1l E33 .- 1. Linear programming I. A tailoring business makes two types of garments A and B. Garment A requires 3 metres of material while garment B requires 2 '1": 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 30 of type B each day. (a) Write down four inequalities from this information. (Smks) {b} Graph these inequalities. (3mks) {c} If the business makes a profit of shs 30 on garment A and a prot of shs 60 on garment B, how many garments of each type must it make in order to maximize the total prot? (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; 301' + 20y s 4800, 30;: + 40y a 3600 and 10x >30y He makes a prot 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 prot (iii) Calculate the maximum prot (iv) If he is to make a weekly prot 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 Ihour on machine B. In one day the lime limit on machine A is 24hours but that on machine B is [2hrs. The number of Jerseys produced must not be more than the shirts produced in one day. The company makes a prot 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 prot and also state the maximum prot 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.?t]. He is prepared to spend not more than shs.2 l .000. It is not viable for hi m 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 prot of shs. 140 while ordinary chairs at a prot of shs. l 20; Determine the maximum possible prot 5. A school has to take 384 people for a tour. There are two types of buses available. Type X and type Y. Type X can carry 6-4 passengers and type Y can carry 48 passengers. They have to use at least 'i' buses. a) Form all linear inequalities which will represent the above information b) 0n the grid provided, draw the inequalities and shade the unwanted region. b} The charges for hiring the buses are ; Type X: shs.25.000 Type Y: shs.20,00() Use your graph to determine the number of buses of each type that should be hired to minimize the cost 6. A shoe maker makes two types of shoes A and B. He takes 3 hours to make one pair of type A and 4 hours to make one pair of type B. He works for a maximum of 120 hours to make it pairs of type A and 3' pairs of type B. It costs him Kshs. 400 to make a pair of type A and Kshs. 150 to make a pair of type B. His total cost does not exceed kshs.9000. He must make at least 8 pairs of type A and 12 pairs of type B. (a) Write down four inequalities representing the information above (b) 0n the grid provided represent the inequalities and shade the unwanted regions to] The shoe maker makes a prot of kshs.40 on each pair of type A and kshs.'i'0 on each pair 7. A theatre has a seating capacity of 250 people. The charges are shs. 100 for an ordinary seat and shs.]tS-['.I for a special seat. It costs shs.16'000 to stage a show and the threatre must make a prot. There is never more than 200 ordinary seats and for a show to take place at least 50 ordinary chairs must be occupied. The number of special seats is always less than twice the number of ordinary seats. a) taking 1 to be the number of ordinary seats and y the number of special seats , write down all the inequalities representing the information above. b} 0n the grid provided, draw the graph to show the inequalities in {a} above c) Determine the number of seats of each type that should be booked in order to maximize the prot. 8. A man sells two types of ice creams in cups and sticks. He can store less than ten packets in his cooling box. He sells more cups than sticks but less than 3 items as many cups as sticks. O 0