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Machine M1 as well as Machine M2 can independently produce either Product P or Product Q. The times taken by machines M1 and M2 (in minutes) to produce one unit of product P and Q are given in the table below: (Each machine works 8 hours per day).

 PRODUCT M1 M2 P 10 8 Q 6 6

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

1. 96
2. 89
3. 100
4. 119

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

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