Question: A company produces two industrial compounds X and Y that are mixed in a final product. They both contain one common input, R. The amount of R in one tonne of X is 8 litres and the amount of R in one tonne of Y is 12 litres. A load of the final product must contain at least 240 litres of R to ensure that its quality level is met. No R is lost in the production process of combining X and Y.
The total cost of a tonne of X is £30 and the total cost of a tonne of Y is £15. If the firm has already signed a contract to buy 7.5 tonnes of X per week, what mix of X and Y should the firm use to minimize the cost of a load of the final product?