The elf Corporation make two brands of hair treatment:Volossy, which is produced

Question

The elf 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 Elf 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.

Formulate using LP

Explanation / Answer

Let 'X' be the profit of Volossy

and 'Y' be the profit of Sedina

Linear programmind problem

Maximize Z = 0.4X + 0.2Y

Subject to the constraints

3X + 4Y < 480 [Colourant stock]

9X + 6Y < 900 [solidifier stock]

X <= 60000 [Production limit of Volossy]

Y >= 20000 [production lower limit of Sedina]

x, y > 0

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