Creepy Chocolate Factory produces two kinds of chocolate drinks (Coco Milk Rich and Coco Milk Lite) that require milk and cocoa powder. The owner wants to determine how many litres of each product to be produced to maximise the profit. For each litre of Coco Milk Rich, 0.7 litres of milk and 150 grams of cocoa powder are required. On the other hand, each litre of Coco Milk Lite requires 0.9 litres of milk and 50 grams of cocoa powder to make. The company has 63 litres of milk and 6 kilograms of coca powder in its inventory. Each litre of Coco Milk Rich, up to 30 litres, gives a profit of $10. Any excess over 30 litres of Coco Milk Rich brings no extra profit. Each litre of Coco Milk Lite gives a profit of $20.
Fun fact: approximately 1 gram of cocoa powder is equal to 0.002 litres.
(a) Formulate the problem as a linear programming (LP) problem.
Hint: Denote X1 as the volume (litres) of Coco Milk Rich and X2 as the volume (litres) of Coco Milk Lite to be produced.
(b) Solve this LP problem graphically. What is the maximum total profit?