A boutique chocolatier has two products: triangular chocolates, called Pyramid (A), and the more decadent chocolates, called Pyramid Deluxe (B).

- Profit from a package of Pyramid is €4.
- Profit from a package of Pyramid Deluxe is €6.

A package of Pyramid requires:
- 0.6 kilos of milk chocolate
- 0.3 kilos of dark chocolate
- 0.03 kilos of nougat

A package of Pyramid Deluxe requires:
- 1.2 kilos of milk chocolate
- 0.2 kilos of dark chocolate
- 0.04 kilos of nougat

Available resources:
- 960 kilos of milk chocolate
- 270 kilos of dark chocolate
- 36 kilos of nougat

What is the maximum possible profit?

A. €1300
B. €1400
C. €1500
D. €1600

The answer can be found by solving a linear programming problem. The variables represent the number of packages of each type of chocolate, and the objective is to maximize profit subject to constraints on the amounts of milk chocolate, dark chocolate, and nougat used. Without solving the problem, it's impossible to determine the correct answer from the provided options.

Explanation:

This problem can be solved using linear programming. Let's denote 'x' as the number of packages of Pyramid (A) and 'y' as the number of packages of Pyramid Deluxe (B). We start defining objective function as: Maximize profit = €4x + €6y. This is the profit equation that we need to find maximum of.

We've the following constraints: 0.6x + 1.2y ≤ 960 (for milk chocolate); 0.3x + 0.2y ≤ 270 (for dark chocolate); and 0.03x + 0.04y ≤ 36 (for nougat). All variables x and y should be more than or equal to 0 as we cannot produce negative packages of chocolates.

Solving this linear programming problem using graphical method or using any mathematical tool like Excel Solver or optimization software will provide the maximum value for profit. Unfortunately, without solving this problem precisely it's impossible to say from provided options (a. €1300 b. €1400 c. €1500 d. €1600) which one is the answer.

Learn more about Linear Programming here:

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