6. ABC Paints company manufactures three grades of paints – Venus, Diana, Aurora. The Plant operates on a three-shift basis and the following data are available from the production records:
Requirement of resource
Grades
Availability (capacity per month)
Venus
Diana
Aurora
Special additive(kgs
per kilolitre)
0.30
0.15
0.75
600 tonnes
Miling (kilolitres per machine shift)
2.0
3.0
5.0
100 machine shifts
Packing
(Kilolitres per shift)
12.0
12.0
12.0
80 shifts
There are no limitations on other resources. The particulars of sale forecasts and estimated contribution to overheads and profits are given below.
Venus
Diana
Aurora
Max possible sales per month
(kilolitres)
100
400
600
Contribution (Rs.
Per kilolitre)
4000
3500
2000
Due to commitments already made a minimum of 200 kilolitres per month of Aurora has to be necessarily supplied during the next year.
Just as company was able to finalize the monthly production programme for the next 12 months an offer was received from a nearby competitor for hiring 40 machine shifts per month of miling capacity for grinding. Diana paint that can be spared for at least a year. However due to additional handling and profit margin of the competitor involved by using this facility, the contribution from Diana will get reduced by 1000 kilolitre. Formulate the linear programming model for determining the monthly production programme to maximize contribution.