Sandy makes $2 profit on every cup of lemonade that she sells and $1 on every cupcake that she sells. Sandy wants to sell at least 5 cups of lemonade and at least 5 cupcakes per day. She wants to earn at least $25 per day. Show and describe all the possible combinations of lemonade and cupcakes that Sandy needs to sell to meet her goals. List two possible combinations.

Question

Sandy makes  $2 profit on every cup of lemonade that she sells and  $1 on every cupcake that she sells. Sandy wants to sell at least 5 cups of lemonade and at least 5 cupcakes per day. She wants to earn at least  $25 per day. Show and describe all the possible combinations of lemonade and cupcakes that Sandy needs to sell to meet her goals. List two possible combinations.

Bytelearn · Accepted Answer

Define Variables and Constraints: Define the variables and the constraints. Let L be the number of cups of lemonade Sandy sells. Let C be the number of cupcakes Sandy sells. Sandy makes $2 profit on every cup of lemonade and $1 on every cupcake. Sandy's goal is to earn at least $25 per day. Sandy wants to sell at least 5 cups of lemonade and at least 5 cupcakes per day. The constraints can be written as: L ≥ 5 C ≥ 5 2L + C ≥ 25Minimum Lemonade Cups: Find the minimum number of lemonade cups Sandy needs to sell to meet the goal without selling any cupcakes. Since Sandy makes $2 profit on every cup of lemonade, we can calculate the minimum number of lemonade cups needed to reach $25 by dividing the goal by the profit per cup of lemonade. Minimum lemonade cups = $25 / $2 per cup = 12.5 cups Since Sandy cannot sell half a cup, she needs to sell at least 13 cups of lemonade to meet the goal without selling any cupcakes.Minimum Cupcakes: Find the minimum number of cupcakes Sandy needs to sell to meet the goal without selling any lemonade. Since Sandy makes $1 profit on every cupcake, we can calculate the minimum number of cupcakes needed to reach $25 by dividing the goal by the profit per cupcake. Minimum cupcakes = $25 / $1 per cupcake = 25 cupcakes Sandy needs to sell at least 25 cupcakes to meet the goal without selling any lemonade.Possible Combinations: List two possible combinations that meet the constraints. Combination 1: Sandy sells 5 cups of lemonade and the rest in cupcakes. Using the equation 2L + C ≥ 25, we substitute L = 5. 2(5) + C ≥ 25 10 + C ≥ 25 C ≥ 25 - 10 C ≥ 15 So, Sandy can sell 5 cups of lemonade and 15 cupcakes to meet her goal.  Combination 2: Sandy sells 6 cups of lemonade and the rest in cupcakes. Using the equation 2L + C ≥ 25, we substitute L = 6. 2(6) + C ≥ 25 12 + C ≥ 25 C ≥ 25 - 12 C ≥ 13 So, Sandy can sell 6 cups of lemonade and 13 cupcakes to meet her goal.

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