I need help with a linear programming word problem?

Question

The problem is: you have 180 tomatoes and 15 onions. You want to use these to make jars of tomato sauce and jars of salsa. A jar of tomato sauce reguires 10 tomatoes and 1 onion. and a jar of salsa requires 5 tomatoes and 1/4 onion. You'll make a profit of $2 on every jar of tomato sauce and $1.50 on every jar of salsa. The farm stand wants at least three times as many jars of tomato sauce as jars of salsa. How many jars of each should you make to maximize the profit?

Answer 1

This doesn't even require much math. Since salsa is far more profitable than tomato sauce, you want to make as much salsa as possible. Alas, the stand wants at least 3 times as much tomato sauce as salsa, so for every jar of salsa you make you MUST provide at least three jars of tomato sauce.

So, for every 3 jars of tomato sauce and 1 jar of salsa you need 35 tomatoes and 3 1/4 onions. That means you can make 12 jars of tomato sauce and 4 jars of salsa, consuming 140 tomatos and 13 onions. You have 40 tomatos and 2 onions left. You can't make any more salsa because there isn't enough material for the required three jars of tomato sauce, so you make two more jars of tomato sauce instead, consuming 20 tomatoes and the last two onions. You now have 14 jars of tomato sauce, 4 jars of salsa, and 20 extra tomatos, which you throw at the farm stand owner for not buying more of your salsa instead of that damn tomato sauce.

Answer 2

first you have to make an equation or two im not sure then you have to find the maximum!