Question

If M1 works at half of its normal efficiency, what is the maximum number of units produced, if at least one unit of each must be produced?

• A. 96
• B. 89
• C. 100
• D. 119

Answer 1

The correct option is D 119

If M1 works at half of its normal efficiency, the time taken by M1 to manufacture 1 unit of P = 20 min and Q = 12 min. And now for the maximum number of units, we have to produce Q on M2 first as it takes only 6 min per piece. Also since at least one unit of P has to be manufactured and it is more efficient to do so on M2 we would do that. So time taken to manufacture 1 unit of P on M2 = 8 min. Hence, time remaining on M2 = (480 - 8) = 472. In this remaining time number of units of Q that can be manufactured $=\frac{472}{6}=78$ (only completed units taken,) Now, since it takes less time to manufacture Q on M1 as well, we will maximize Q on M1. Since 1 unit of number of units that can be produced $=\frac{8\times 60}{12}=40.$ Hence, total number of units manufactured = (1 + 78 + 40) = 119 units.