A sugar company produces brown sugar, white sugar, powdered sugar, and treacle from sugar cane syrup. The company purchases 3200 tonnes of syrup weekly and is contracted to deliver at least 70 tonnes weekly of each type of sugar.
The production process starts by manufacturing brown sugar and treacle from the syrup. A tonne of syrup produces 0.35 tonne of brown sugar and 0.2 tonne of treacle. Next white sugar is produced by processing brown sugar. It takes 1 tonne of brown sugar to produce 0.8 tonne of white sugar.
Finally, powdered sugar is produced from white sugar. It takes 1 tonne of white sugar to produce 0.85 tonne of powdered sugar.
The profit per tonne (sold) for brown sugar, white sugar, powdered sugar, and treacle is £130, £260, £300, and £50, respectively.
What is the maximal weekly profit that the company can achieve by designing an optimal production plan?