Linear programming questions | form four Basic Mathematics

A certain secondary school intends to buy two types of Basic Mathematics reference books. The school wants between 10 and 15 books (inclusive) of author A which cost 8,000/= each. Books from author B cost I 0,000/= each. If the school has 240,000/=, what is the maximum number of books can the school buy?

Two types of products namely A and B are manufactured on machines M1 and M2. The following table shows the requirements for the production of these products.

A small industry makes two types of clothes namely type A and type B. Each type A takes 3 hours to produce and uses 6 metres of material and each type B takes 6 hours to produce and uses 7 metres of material. The workers can work for a total of 60 hours and there is 90 metres of material available. If the profit on a type A cloth is 4,000 shillings and on a type B is 6,000 shillings, find how many of each type should be made for maximum profit.

A school is preparing for trip of 360 students. The company providing the transport has 12 buses of 45 seats each and 8 buses of 30 seats each and has only 10 drivers available . The rental cost for a large bus is 648,000 shillings and 500,000 shillings for the small bus. How many buses each type should be used for minimum cost ?

A farmer has 20 hectares for growing tomatoes and cabbages. The cost per hectare for tomatoes is sh 48,000 and for cabbages is sh 32,000. The farmer has budgeted sh 768,000. Tomatoes require one manday per hectare and   cabbages require two mandays per hectare. There are 36 mandays available. The profit on tomatoes is sh 160,000 per hectare and on cabbages is sh 192,000 per hectare. Find the number of hectares of each crop the farmer should plant to maximize the profit.

A businessman plans to buy at most 210 sacks of Irish and sweet potatoes. Irish potatoes cost shs. 30,000 per sack and sweet potatoes cost shs. 5,000 per sack. He can spend up to shs. 2,500,000 for his business. The profit on a single sack of Irish potatoes is shs. 12,000 and for sweet potatoes is shs. 10,000. How many sacks of each type of potatoes the businessman will buy in order to realize the maximum profit?

A trader has a space for 5 refrigerators. The trader plans to spend 2,400,000 shillings to buy refrigerators of two brands, Hitachi and Sony. Each Hitachi refrigerator costs 600,000 shillings whereas each Sony refrigerator costs 400,000 shillings. The unit profits for Hitachi and Sony refrigerators are 200,000 shillings and 150,000 shillings respectively. Denoting ​ x and ​ y as the number of Hitachi and Sony refrigerators respectively, determine the number of refrigerators for each brand that maximizes profit.

A farmer needs to buy up to 25 cows for a new herd. He can buy either brown cows at 50,000/= each or black cows at 80,000/= each and he can spend a total of not more than 1,580,000/=. He must have at least 9 cows of each type. On selling the cows he will make a profit of 5,000/= on each brown cow and 6,000/= on each black cow. How many of each type he should buy to maximize profit?

Zelda wants to buy oranges and mangoes for her children. The oranges are sold at sh. 150 each and mangoes at sh. 200 each. She must buy at least two of each kind of fruit but her shopping bag cannot hold more than 10 fruits. If the owner of the shop makes a profit of sh. 40 on each orange and sh. 60 on each mango, determine how many fruits of each kind Zelda must buy for the shop owner to realise maximum profit.

A shopkeeper sells refrigerators and washing machines. Each refrigerator takes up 1.8m​² of space and costs 300,000 shillings; whereas each washing machine takes up 1.5m^​2 of space and costs 500,000 shillings. The owner of the shop has 6,000,000 shillings to spend and has 27m^2​ of space.

1. Write down all the inequalities which represent the given information.
2. If he makes a profit of 30,000 shillings on each refrigerator and 40,000 shillings on each washing machine, find how many refrigerators and  washing machines he should sell for maximum profit.