Page 136 - DCAP601_SIMULATION_AND_MODELING

Simulation and Modelling

Notes


Caselet LP Model in a Paint Company

ENTON Paints Ltd manufactures three grades of paints — Venus, Diana and Aurota.
The plant operates on a three-shift basis and the data presented in Table 1 are made
Favailable from the production records.

Table 1

There are no limitations on other resources. The particulars of sale forecasts and estimated
contribution to overheads and profits are given in Table 2.

Table 2

Due to commitments already made, a minimum of 200 kilolitres per month of Aurota has
to be necessarily supplied the next year. Just as the company was able to finalise the
monthly production programme for the next 12 months, an offer was received from a
nearby competitor for hiring 50 machine shifts per month of milling capacity for grinding
Diana paint, that can be spared for at least a year.
However, due to additional handling and the profit margin of the competitor
involved, by using this facility, the contribution from Diana will get reduced by ` 1.50 per
litre.

Formulate this problem as a linear programming (LP) model for determining the monthly
production programme to maximise contribution. You are not required to solve the LP
model.
Let x litres of Venus grade paint, y litres of Diana grade paint and
Table 3

z litres of Aurota grade paint be manufactured as shown in Table 3.
Maximisation of contribution:
Maximise z = 4x + (3.6 - 1.5)y + 2.5z
z = 4x + 2.1y + 2.5z Contd...

130 LOVELY PROFESSIONAL UNIVERSITY