The Ooze Haircraft Corporation make two brands of hair treatment: Volossy, which is produced under licence, and its own products Sedina. The company is in dispute with its supplier of colourant and solidifier as a result of which the supplier is no longer taking their orders. An alternative source of supply cannot be arranged for a month and Ooze must plan production for the month with their stock of 480 litres of colourant and 900 litres of solidifier.
A bottle of Volossy requires 3 millilitres of colourant and 9 millilitres of solidifier. A bottle of Sedina requires 4 millilitres of colourant and 6 millilitres of solidifier. The licensing agreement restricts production of Volossy to no more than 60,000 bottles a month and commitments to existing customers mean that at least 20,000 bottles of Sedina must be produced.
The company makes £0.40 profit per bottle of Volossy and £0.20 profit per bottle of Sedina.
(a) How many bottles of each product should they produce and how much profit will they make?
(b) Identify which constraints are tight and which are slack.