27. A factory is engaged in producing two items, / 1 and / 2, each of which has to pass through three machinesM1, M2 andM3. One unit of/1 requires one hour of machining onM1, 2 hours onM2 and 1 hour on M3, while one unit of /2 requires machining of an hour each on M1 and M2, and 3 hours on M3• In a week, a maximum of 40 hours on machine M1, 70 hours on M2, and 90 hours on machine M3 are available. It is given that the per unit profit on /1 is Rs 40 and that on /2 is Rs 60.

The present production mix of the factory is: /1 30 units and /2 10 units, per week. This implies that the present profit of the factory is Rs 1,800 a week. Also, machines M1 andM2 are being fully utilised.

In your opinion, is the present production mix optimal? If not, specify' what should it be and find the increase in profit that would result if the new mix determined by you is adopted. Also determine the time for which some machine(s) may be idle in respect of the mix suggested by you.