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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?

- 96
- 89
- 100
- 119

1 vote

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**