Question

Your coffee bar has two kinds of drink. One cup of the first one costs 9 grams of juice, 4 grams of coffee and 3 grams of sugar. The second one costs 4 grams of juice, 5 grams of coffee and 10 grams of sugar. The budget is at most 3.6 kilograms of juice, 2.0 kilograms of coffee and 3.0 kilograms of sugar every day. You get $1.2 if you sell one cup of the first kind of drink and $0.7 of the other one. What is the maximum profit? How many drinks should be sold to get a maximum profit?

Answer 1

To find the maximum profit and the number of drinks that should be sold to achieve this maximum profit, we can use linear programming.

Step-by-step explanation:

To find the maximum profit and the number of drinks that should be sold to achieve this maximum profit, we can use linear programming. Let x be the number of cups of the first drink and y be the number of cups of the second drink sold.

The objective function to maximize profit is given by:

P = 1.2x + 0.7y

The constraints are:

• 9x + 4y ≤ 3600 (Juice constraint)
• 4x + 5y ≤ 2000 (Coffee constraint)
• 3x + 10y ≤ 3000 (Sugar constraint)
• x ≥ 0 (Non-negativity constraint for the first drink)
• y ≥ 0 (Non-negativity constraint for the second drink)

Solving this linear programming problem will give us the maximum profit and the corresponding values of x and y.