Linear programming questions | form four Basic Mathematics

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?

Answer / Solution

UNSOLVED

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.

Answer / Solution

UNSOLVED

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?

Answer / Solution

UNSOLVED

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.

Answer / Solution

UNSOLVED

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.

Answer / Solution

UNSOLVED