need help finding buffer size, throughput rate, total time, and wgat is the total production time for $100$ pieces

In this assignment, we will practice the following essential metrics in the production design to

Understand balancine a produ

We nould determine the buffer sixe, throughput rate, and total cost as follows:

$-$ Buffer size:

To balanee the production line

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Step $1$

Based on the information provided, the buffer size is $86,$ the throughput rate is $0\mathrm{.}29$ pieces$/$minute$,$ the total production time for the batch size of $100$ pieces is $583\mathrm{.}3$ hours, and the total cost of the line operating two shifts with one operator per section would be calculated as follows:

Explanation:

Manufacturing cost: $100$ pieces $*10$ cents$/$piece $=$ $$10$

Labor cost: $2$ shifts $*10$ dollars$/$hour $*583\mathrm{.}3$ hours $=11,666\mathrm{.}6$ dollars

Fixed cost: $2$ shifts $*20$ dollars$/$day $*(583\mathrm{.}3/24)$ days $=4,166\mathrm{.}7$ dollars

Overhead cost: $(10+11,666\mathrm{.}6+4,166\mathrm{.}7)*15\%=2,250$ dollars

Total cost: $10+11,666\mathrm{.}6+4,166\mathrm{.}7+2,250=28,083\mathrm{.}3$ dollars.

Step $2$

Based on the information provided, the buffer size between work centers $1$ and $2$ would be:

Buffer size $=100*(1-100/350)*1\mathrm{.}2$

$=100*(0\mathrm{.}71)*1\mathrm{.}2$

$=86$

Explanation:

The throughput rate would be:

Throughput rate $=100/350$

$=0\mathrm{.}29$ pieces$/$minute

Step $3$

The total production time for the batch size of $100$ pieces would be:

Total production time $=100/0\mathrm{.}29$

$=350$ minutes

$=5\mathrm{.}83$ hours $($approx$.5$ hours and $50$ minutes$)$

Explanation:

The total cost of the line operating two shifts with one operator per section would be:

Materials cost $=10$ cents $*100$ pieces $=10$ dollars

Labor cost $=10$ dollars$/$hour $*5\mathrm{.}83$ hours $=58\mathrm{.}3$ dollars

Fixed cost $=20$ dollars $*2$ shifts $=40$ dollars

Overhead $=15\%*(10$ dollars $+58\mathrm{.}3$ dollars $+40$ dollars$)=11\mathrm{.}73$ dollars

Answer

Total cost $=10$ dollars $+58\mathrm{.}3$ dollars $+40$ dollars $+11\mathrm{.}73$ dollars $=120\mathrm{.}03$ dollars