Linear programming help

Question

Sophia grows and sells tomatoes and beans. It costs 1 dollar to a grow a bushel of tomatoes and 2 square yard of land. it costs 3 dollars to grow a bushel of beans and it takes 4 square yards of land. Sophia has a total of $15 and 24 square yards ofd land. She must plant at least one bushel of tomatoes but not more than 8 bushels. She must plant at least 1 bushel of green beans. if she makes $2 profit on a bushel of tomatoes and $5 on a bushel of beans, how many bushels of each should she grow?

Answer 1

8 years late but, better late than never, right?

First we need to indentify our objective function, (what are we trying to achieve), and that is to maximize the profit for Sophia. Let x_T represent tomatoes and x_B represent beans.

Maximize Profit: 2 x_T + 5 x_B

Next we establish our constraints, which are sq. yards available, money available, and individual crop requirements.

Yards : 2 x_T + 4 x_B ≤ 24

Budget: x_T + 3 x_B ≤ 15

Tomatoes: 1 ≤ x_T ≤ 8

Beans: 1 ≤ x_B

Then its either trail and error at this point or taking it to a computer.

I actually did a full deep-dive into this specific problem—from setting up the logic to running the Python code to find the optimal solution

You can watch the full walkthrough here: Can you help Sophia with her farming problem? | Linear Programming