M1 works at half of its normal efficiency - time taken to manufacture P by M1 will be 10*2 min = 20 min
& time taken to manufacture Q by M1 will be 6*2 min = 12 min
time taken to manufacture P by M2 8 min
time taken to manufacture Q by M2 6 min
As, at least one unit of each product must be produced - one unit of product P will be manufactured by M2 as it takes less time to produce it.
So, time taken to produce one unit of product by M2 is 8 min
In the remaining time ((8 * 60) - 8) = 472 min M2 will produce product Q as it takes less time than product P
So, In the remaining 472 mins, M2 will produce $\dfrac{472}{6}$ = 78.6 units ≅ 78 units of product Q
Total units produced by M2 in 8 hrs = (1 + 78) = 79 units
Now, m/c M1 can produce maximum $\dfrac{{8}*{60}}{12}$ = 40 units .
So, The maximum number of units produced, if at least one unit of each must be produced will be (79 + 40) units = 119 units