Question

Cherries cost $4/lb. Grapes cost $2.50/lb. You can spend no more than $15 on fruit, and you need at least 4 lb in all. Create a graph showing the amount of each fruit you can buy.

Answer 1

To create a graph showing the amount of each fruit you can buy, we will consider the possible combinations of buying cherries (x-axis) and grapes (y-axis) within the given constraints.

Let's start by creating a table with some possible combinations of buying cherries and grapes:

| Cherries (lbs) | Grapes (lbs) |
|----------------|--------------|
| 0 | 6 |
| 1 | 5 |
| 2 | 4 |
| 3 | 3 |
| 4 | 2 |
| 5 | 1 |
| 6 | 0 |

Now, let's calculate the cost for each combination and exclude the ones that exceed $15:

| Cherries (lbs) | Grapes (lbs) | Cost ($) |
|----------------|--------------|----------|
| 0 | 6 | $15.00 |
| 1 | 5 | $14.50 |
| 2 | 4 | $14.00 |
| 3 | 3 | $13.50 |
| 4 | 2 | $12.00 |
| 5 | 1 | $10.50 |
| 6 | 0 | $8.00 |

Now, we can plot the graph with the Cherries (lbs) on the x-axis and Grapes (lbs) on the y-axis. We will only include the valid combinations within the area that satisfies both constraints.

```
|
6 | *
| |
5 | * |
| |
4 | * |
| |
3 | * |
| |
2 | * |
| |
1 | * |
| |
0 | * |
-------------------
0 6
```

In the graph above, the asterisks (*) represent the valid combinations that meet the given constraints. The x-coordinate represents the amount of cherries (lbs) and the y-coordinate represents the amount of grapes (lbs).