Check mynicknameisnickname they have this question for 100 points for the first correct person cartesian cola is a very popular drinks brand among mathematicians. they sell two products. a bottle of cartesian cola classic contains 500ml water, 600g sugar, and 0.1g caramel. a bottle of cartesian cola quantum contains 550ml water, 200g sugar, and 0.2g caramel. even though demand for their products is virtually unlimited, every day they are limited to 100 litres of water, 100kg of sugar and 32g caramel. for each bottle sold, cartesian cola classic makes 40p profit, and cartesian cola quantum makes 19p profit. how many bottles of each should cartesian cola produce each day to maximise their profit, and what is the profit per day?

Let "c" and "q" represent the numbers of bottles of Classic and Quantum that should be produced each day to maximize profit. The problem conditions give rise to 3 inequalities:
.. 0.500c +0.550q ≤ 100 . . . . . . . liters of water
.. 0.600c +0.200q ≤ 100 . . . . . . . kg of sugar
.. 0.1c +0.2q ≤ 32 . . . . . . . . . . . . . grams of caramel
These can be plotted on a graph to find the feasible region where c and q satisfy all constraints. You find that the caramel constraint does not come into play. The graph below has c plotted on the horizontal axis and q plotted on the vertical axis.

Optimum production occurs near c = 152.17 and q = 43.48. Examination of profit figures for solutions near those values reveals the best result for (c, q) = (153, 41). Those levels of production give a profit of 6899p per day.

To maximize profit, Cartesian Cola should produce each day
.. 153 bottles of Classic
.. 41 bottles of Quantum per day.

Profit will be 6899p per day.

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The problem statement gives no clue as to the currency equivalent of 100p.