Answer:
The farmer should plant 20 acres with crop A and 30 acres with crop B for maximum profit.
Step-by-step explanation:
Total land of farmer = 50 acre
Cost of seed for crop A = $10 per acre
Cost of seed for crop B = $5 per acre
Total amount to be spent on seeds = $350
Profit on crops by seed A = $250 per acre
Profit on crops by seed B= $100 per acre
Let the farmer plants x acre with seeds A.
and the farmer plants y acre with seeds B.
Now, according to the question:
x + y = 50
and 10 x + 5 y = 350
To MAXIMIZE: 250x + 100y
Solving the system of the equations, we get
10 x + 5(50 - x) = 350
or, x = 20
Putting this in x+ y = 50, we get y= 30
Hence,x= 20,y = 30 is the solution for the set of equations
So, Profit = 250 (20) + 100(30) = 5,000 + 3,000 = $8,000 (MAXIMUM)
Hence, farmer should plant 20 acres with crop A and 30 acres with crop B for maximum profit.