Final answer:
To maximize profit, the farmer can set up a linear programming problem with constraints on the number of animals and the cost. By solving the linear programming problem, the farmer can determine the optimal number of cows and sheep to raise and the maximum profit he can make.
Step-by-step explanation:
The farmer wants to maximize his profit by raising cows and sheep. He wants to raise no more than 16 animals, including no more than 12 sheep. To find the maximum profit, we need to determine the number of cows and sheep he should raise. Let's assume he raises x cows and y sheep.
The cost to raise a cow is Br 5 and the cost to raise a sheep is Br 2, and the farmer has Br 50 available. So, the cost equation can be written as 5x + 2y = 50.
The revenue from selling a cow is Birr 100 and the revenue from selling a sheep is Birr 50, so the revenue equation can be written as 100x + 50y.
Using the constraints of the problem, we can set up the following linear programming model:
Maximize 100x + 50y
Subject to:
x + y ≤ 16 (maximum total number of animals)
y ≤ 12 (maximum number of sheep)
5x + 2y ≤ 50 (maximum cost)
x ≥ 0 (non-negative number of cows)
y ≥ 0 (non-negative number of sheep)
Solving this linear programming problem will give us the values of x and y that maximize the profit.