Question

Define the variable you will use in your model

you have a budget of 40$ fruit cost 4$ per pound and the granola bars cost 1$ each and i need to buy at least 20 of them. what combination of fruit and granola bars can you buy?

Answer 1

Explanation:

Let x represent the number of pounds of fruit that you can buy.

Let y represent the number of pounds of fruit that you can buy.

You need to buy at least 20 of them. This means that

x + y ≥ 20 - - - - - - - - - - - 1

You have a budget of 40$. Fruit cost 4$ per pound and the granola bars cost 1$ each. This means that

4x + y = 40

Substituting y = 40 - 4x into equation 1, it becomes

x + 40 - 4x ≥ 20

x - 4x ≥ 20 - 40

- 3x ≥ - 20

Dividing both sides of the equation by - 1, it becomes

3x ≤ 20

x ≤ 20/3 = 6.67

This means that the maximum number of pounds of fruit that you can by is 6 pounds.

Therefore the combination of fruit and granola bars that you can buy would be

1) 6 pounds of fruit and 16 bars of granola.

2) 5 pounds of fruit and 20 bars of granola.

3) 4 pounds of fruit and 24 bars of granola.

4) 3 pounds of fruit and 28 bars of granola.

5) 2 pounds of fruit and 32 bars of granola.

6) 1 pound of fruit and 36 bars of granola.