Please help me i dont know how to solve this word problem

Question

A farmer is going to divide her 50 acre farm between two crops. Seed for crop A costs $25 per acre. Seed for crop B costs $50 per acre. The farmer can spend at most $1500 on seed. 

If crop B brings in a profit of $110 per acre, and crop A brings in a profit of $80 per acre, how many acres of each crop should the farmer plant to maximize her profit?

Answer 1

A farmer is going to divide her 50 acre farm between two crops.

Let's say x is the acres for crop A and y the acres for crop B. The total acres is 50:

x + y = 50

Or

x = 50 - y

If crop B brings in a profit of $110 per acre, and crop A brings in a profit of $80 per acre, how many acres of each crop should the farmer plant to maximize her profit?

Profit is

P = y*110 + x*80

Let's substitute, x = 50 - y to find P in terms of y only

P = 110*y + 80*(50-y)

P = 110*y + 4000 - 80*y

P = 30*y + 4000

This equation says that the more crop B she plants, the more profit she will make. But, there is another constraint:

Seed for crop A costs $25 per acre. Seed for crop B costs $50 per acre. The farmer can spend at most $1500 on seed. 

Cost of seeds will be:

x*25 + y*50

And this needs to be less then or equal to $1500

x*25 + y*50 <= 1500

Let's substitute x = 50 - y in this inequality

25*(50 - y) + 50*y <= 1500

1250 - 25*y + 50*y <= 1500 (combine y terms and add -1250 to both sides)

25*y <= 250 (divide both sides by 25)

y <= 10

So, y can be at most 10. Since P is increases as y increases (P = 30*y + 4000), y must be 10 or 10 acres for crop B

x = 50 - y = 50 -10 = 40 or 40 acres for crop A

Profit will be

P = 110*10 + 80*40 = 1100 + 3200 = $4300

Answer 2

A farmer is going to divide her 50 acre farm between two crops. Seed for crop A costs $25 per acre. Seed for crop B costs $50 per acre. The farmer can spend at most $1500 on seed. 

If crop B brings in a profit of $110 per acre, and crop A brings in a profit of $80 per acre, how many acres of each crop should the farmer plant to maximize her profit?

Profit=Revenue-Cost

P=R-C

His cost, C, is C=($25/acre)A_a+($50/acre)A_b≤$1500

His profit, P, is P=($110/acre)A_a+($80/acre)A_b

Set 25A_a+50A_b=1500

A_a=(1500-50A_b)/25=60-2A_b

Substitute this into the profit equation:

110(60-2A_b)+80A_b=P

6600-220A_b+80A_b=P

P=6600-140A_b

So his profit, P, is maximized if he plants no seeds for crop B and plants them all for crop A. He needs to plant seeds in 60 acres of crop A.