Afarmer is going to divide her 50 acre form between two crops seed for crop a cost $10 per acre seed for crabby cost five dollars per acre the farmer can spend at most $350 on seed if crop be brings in a profit of $100 per acre in crop a brings in a profit of 250 per acre how many acres of each crops of the farmer plant to maximize your profit

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.