Question

A commuter airline makes lattes in the galley and sells them to passengers. A regular latte contains a shot of espresso, 1 cup of 2% milk, steamed, and 0.5 cup of whipped cream. The low-fat latte contains a shot of espresso, 1.25 cups of skim milk, frothed, and no whipped cream. The plane begins its journey with 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream. The airline makes a profit of $1.58 on each regular latte and $1.65 on each low-fat latte. Assuming that all lattes that are made can be sold, what would be the ideal mix of regular and low-fat lattes to maximize the profit for the airline?

Answer 1

To maximize profit, the airline should make 60 regular lattes and 48 low-fat lattes.

Step-by-step explanation:

To determine the ideal mix of regular and low-fat lattes to maximize the profit for the airline, we need to find the number of regular and low-fat lattes that can be made using the available ingredients, and then calculate the profit for each combination. The airline has 100 shots of espresso, 60 cups of skim milk, 60 cups of 2% milk, and 30 cups of whipped cream.

Let's start by calculating the number of regular lattes that can be made. Each regular latte requires 1 shot of espresso, 1 cup of 2% milk, and 0.5 cup of whipped cream. With the available ingredients, we can make a maximum of 60 regular lattes.

Next, let's calculate the number of low-fat lattes that can be made. Each low-fat latte requires 1 shot of espresso, 1.25 cups of skim milk, and no whipped cream. With the available ingredients, we can make a maximum of 48 low-fat lattes.

Now, let's calculate the profit for each combination. The profit for each regular latte is $1.58, and the profit for each low-fat latte is $1.65.

Multiplying the number of regular lattes by the profit per regular latte and the number of low-fat lattes by the profit per low-fat latte, we can calculate the total profit for each combination. The combination that maximizes the profit for the airline is the one with the highest total profit.

Answer 2

To maximize profit, the amount of each type of coffees made are;

The number of regular latte made = 52 cups

The number of low-fat latte made = 48 cups

Step-by-step explanation:

The given parameters are;

The number of espresso in a regular latte = 1 shot

The number of cups of 2% milk in regular latte = 1 cup

The amount of whipped cream in a regular latte = 0.5 cup

The number of cups of skim milk in the low-fat latte = 1.25 cup

The number of espresso in a low-fat latte = 1 shot

The amount of whipped cream in a low-fat latte = 0 cup

The number of cups of espresso in the journey = 100 shots

The number of cups of skim milk in the journey = 60 cups

The number of cups of 2% milk in the journey = 60 cups

The amount of profit the airline makes on each regular latte = $1.58

The amount of profit the airline makes on each low-fat latte = $1.65

Let 'x' represent the number regular lattes made and let 'y' represent the number low-fat lattes made, we have;

x ≤ 30/0.5 = 60

x ≤ 60

y ≤ 60

y ≤ 60/1.25 = 48

∴ y ≤ 48

x + y ≤ 100

Therefore, the given that more profit is made from the sale of low-fat latte than for regular latte, the maximum number of low-fat latte should be made

Therefore, the number of low-fat latte made, y = 48

Therefore, the number of regular latte made, x ≤ 100 - 48 = 52

For maximum profit, the maximum number of low-fat latte, 'x', should be made

Therefore, x = 52

The ideal mix of regular and low-fat lattes to maximize profit is 52 cups of regular latte and 48 cups of low-fat latte