Question

A factory makes soft drinks, specialising in Coca-Cola and Lemonade. The main ingredients are water and sugar. A case of Lemonade requires 9 litres of water and 0.6 kilograms of sugar. A case of Coca-Cola requires 9 litres of water and 0.9 kilograms of sugar. The factory has 900 litres of water and 72 kilograms of sugar available to make cases of soft drinks. A case of Lemonade yields a $3 profit, and a case of Coca-Cola yields a $4 profit. The factory wants to determine the number of cases of each soft drink to produce in order to maximise profit. The numbers of cases are not required to be integers. In this question you must calculate all answers manually, showing all working. In part (e) you are also required to check your work using a linear programming tool. Formulate a linear programming model for this problem.

Answer 1

The linear programming model for this problem is to maximize the profit by producing a certain number of cases of Lemonade and Coca-Cola, subject to constraints on the available water and sugar.

Step-by-step explanation:

The problem can be solved using linear programming techniques. Let's define the decision variables:

x = number of cases of Lemonade

y = number of cases of Coca-Cola

The objective is to maximize the profit, which is given by:

Profit = 3x + 4y

Now, let's set up the constraints:

Water constraint: 9x + 9y <= 900

Sugar constraint: 0.6x + 0.9y <= 72

Non-negativity constraint: x >= 0 and y >= 0

The linear programming model for this problem is:

Maximize 3x + 4y

Subject to:

9x + 9y <= 900

0.6x + 0.9y <= 72

x, y >= 0