Two different machines are used to manufacture a product. The first machine makes the top part, 14 in each batch, and the second machine makes the bottom part, 16 in each batch. Each top part is assembled with the bottom part and released to the sales department. Find the minimum number of product needs to be produced such that no unassembled parts are left.

Open in App

Solution

The $1^{s t}$ machine produces $14$ top parts in a batch.
The $2^{n d}$ machine produces $16$ bottom parts in a batch.

It is given that no unassembled parts are left.
$∴$ Number of assembled products is a common multiple of $14$ and $16.$
$\Rightarrow$ The minimum number of assembled products is the least common multiple of $14$ and $16.$

Using ladder diagram,
LCM $= 2^{4} \times 7 = 112$

$∴$ Required number of assembled products is $112.$

For this, first machine have to make 8 batches and second machine have to make 7 batches.

Suggest Corrections

Similar questions

Q. Two different machines are used to manufacture a product. The

1^{s t}

machine makes the top part,

14

in each batch, and the

2^{n d}

machine makes the bottom part,

16

in each batch. Each top part is assembled with the bottom part and released to the sales department.

Find the minimum number of batches needs to be produced by the

2^{n d}

machine such that no unassembled parts are left.

Q. A firm uses a turning center, a milling center and a grinding machine to produce two parts. The table below provides the machining time required for each part and the maximum machining time available on each machine. The profit per unit on parts I and II are Rs 40 and Rs 100, respectively. The maximum profit per week of the firm is Rs

Type of mchine	Machining time required for the machine part (minutes)		Maximum machining time available per week (minutes)
	I	II
Turning Center	12	6	6000
Milling Center	4	10	4000
Grinding Machine	2	3	1800

Q. At a production machine, parts arrive according to a Poisson process at the rate of 0.35 parts per minute. Processing time for parts has an exponential distribution with mean of 2 minutes. What is the probability that a random part arrival finds that there are already 8 parts in the system (in machine + in queue)?

Q. A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at ₹7 profit and that of B at a profit of ₹4. Find the production level per day for maximum profit graphically.

An article manufactured by a company consists of two parts X and Y. In the process of manufacture of part X, 9 out of 104 parts may be defective. Similartly, 5 out of 100 are likely to be defective in the manufacture of the part Y. Calculate the probability that the assembled product will not be defective.

Join BYJU'S Learning Program