Question

A small scale farmer wishes to buy some sheep and goats for rearing. A sheep costs sh.400, and a goat costs sh.300. The farmer has enough space for only 20 animals and may spend at most sh.6800. The number of goats should not exceed twice the number of sheep.

a) By letting x and y represent the number of sheep and goats he can buy respectively, write down all inequalities from the above information. (4 marks)
a) 400x + 300y ≤ 6800
b) x + y ≤ 20
c) y ≤ 2x
d) All of the above

Answer 1

A farmer faces constraints on budget and animal housing capacity when buying sheep and goats. The three inequalities represent the maximum expenditure, the limited space for animals, and the goat-to-sheep ratio constraint.

Step-by-step explanation:

The inequalities that represent the financial and spatial constraints of the farmer who wishes to buy sheep and goats are as follows:

• a) 400x + 300y ≤ 6800
• b) x + y ≤ 20
• c) y ≤ 2x

The farmer can use these inequalities to determine how many sheep (x) and goats (y) can be bought without exceeding the budget of sh.6800 and the limit of 20 total animals, and ensuring the number of goats does not exceed twice the number of sheep.