Quesstions on LP , help asap
10. The games master whishes to hire two matatus for a trip. The operators have a Toyota which carries 10passengers and a Kombi which carries 20 passengers. Altogether 120 people have to travel. The operators have only 20litres of fuel and the Toyota consumes 4 litres on each round trip and the Kombi 1 litre on each round trip. If the Toyota makes x round trips and the kombi y round trips; (a) write down four inequalities in x and y which must be satisfied bj represent the inequalities graphically on the grid provided 24 (c) The operators charge shs. 100 for each round trip in the Toyota and shs.300 for each round trip in the kombi; (i) determine the number of trips made by each vehicle so as to make the total cost a Minimum (ii) find the minimum cost6. 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 x pairs of type A and y 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) On the grid provided represent the inequalities and shade the unwanted regions (c) The shoe maker makes a profit of kshs.40 on each pair of type A and kshs.70 on each pair 7. A theatre has a seating capacity of 250 people. The charges are shs. 100 for an ordinary seat and shs. 160 for a special seat. It costs shs. 16,000 to stage a show and the threatre must make a profit. 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 x to be the number of ordinary seats and y the number of special seats , write down all the inequalities representing the information above. b) On 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 profit. 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. He also knows that he will sell more than 3 packets of sticks. His profit is shs.3.00 on a packet of cups and shs.2.00 on a packet of sticks. (a) Form inequalities to represent the above information: (Let x - packets of cups and y - packets of sticks) (b) On the grid provided graph the inequalities to satisfy the required condition (c) How many packets of cups and sticks should the man put in his box to give him the highest profit? 9. A shopkeeper bought 50 pangas and 30 jembes :- (a) From a wholesalers for shs.4.260. He had bought half as many jembes and 5 pangas less, he would have paid shs. 1290 less. Had the shopkeeper bought form wholesaler B, he would have paid 10% more a panga and 15% less for a jembe. How much would he have saved if he had bought the 50pangas and 30 jembes from wholesalers B (b) The price of a suit if marked at shs.5000. A discount
