Question

You plan to start a baking company that sells donuts and cupcakes. You have space in your fridge to store at most 40 baked goods. Each donut sells for 2 and each cupcake sells for 3. You need to sell at least 60 a week to make a profit.

How many combinations of donuts and cupcakes can you sell in a week to make a profit of at least 60?

A) 20 donuts and 10 cupcakes
B) 15 donuts and 15 cupcakes
C) 10 donuts and 20 cupcakes
D) 5 donuts and 25 cupcakes

Answer 1

All the given options (A, B, C, and D) meet both the storage constraint of at most 40 baked goods and the revenue constraint to make at least $60 profit. Therefore, each can be a valid combination to achieve the minimum profit required.

Step-by-step explanation:

To determine the combinations of donuts and cupcakes that can be sold to make a profit of at least $60 a week, we need to set up inequalities that represent the constraints given in the problem. The constraint of having space for at most 40 baked goods in the fridge can be represented as:

D + C ≤ 40

where D represents the number of donuts and C represents the number of cupcakes.

To find the revenue from selling donuts and cupcakes, we use the selling prices of $2 for each donut and $3 for each cupcake. The revenue constraint to make at least $60 in profit can be represented as:

2D + 3C ≥ 60

Now, let's evaluate the provided options:

• A) 20 donuts and 10 cupcakes:
  Revenue = 2(20) + 3(10) = $70
• B) 15 donuts and 15 cupcakes:
  Revenue = 2(15) + 3(15) = $75
• C) 10 donuts and 20 cupcakes:
  Revenue = 2(10) + 3(20) = $80
• D) 5 donuts and 25 cupcakes:
  Revenue = 2(5) + 3(25) = $85

All the given options satisfy the space constraint as the sum of donuts and cupcakes does not exceed 40. Additionally, all options meet the revenue constraint since they all result in a profit of $60 or more.