Question

Joaquín runs a bakery that sells two kinds of cookies. Joaquín knows the bakery must make at least 47 and at most 78 boxes of the Mint Breezes. The bakery must also make between 3 and 80 boxes of the Fluffy Deliciousness. The boxes of Mint Breezes take 5 ounces of sugar, while boxes of Fluffy Deliciousness require 3 ounces of sugar. The bakery only has 540 ounces of sugar available. If boxes of Mint Breezes generate $6.00 in profit, and boxes of Fluffy Deliciousness generate $10.00, how many boxes of the cookies should Joaquín have the bakery make to get the most profit? Mint Breezes: Fluffy Deliciousness: Best profit:

Answer 1

To maximize profit, Joaquín should make the number of boxes of Mint Breezes that generates the most profit and the number of boxes of Fluffy Deliciousness that generates the most profit, given the available sugar. Mathematical optimization techniques, such as linear programming, can be used to solve this problem.

Step-by-step explanation:

To maximize profit, Joaquín should make the number of boxes of Mint Breezes that generates the most profit and the number of boxes of Fluffy Deliciousness that generates the most profit, given the available sugar.

Let's assume x represents the number of boxes of Mint Breezes and y represents the number of boxes of Fluffy Deliciousness.

To determine the number of boxes that generate the most profit, we can use a mathematical optimization technique called linear programming.

1. Constraint 1: 5x + 3y ≤ 540 (availability of sugar in ounces)
2. Constraint 2: 47 ≤ x ≤ 78 (minimum and maximum number of Mint Breezes boxes)
3. Constraint 3: 3 ≤ y ≤ 80 (minimum and maximum number of Fluffy Deliciousness boxes)
4. Objective function: Maximize 6x + 10y (profit in dollars)

By solving this linear programming problem, we can find the values of x and y that will result in the highest profit.