Question $1$

$1\mathrm{.}1$ A small electrical appliance is to be produced on a single$-$model assembly line. The work

content of assembling the product has been reduced to the work elements listed in Table A$.$

The table also lists the times for each element and the precedence order in which they must

be performed. The line is to be balanced for an annual demand of $150000$ units each year.

The line will operate $50$ week a year, $5$ straight shifts per week. These shifts take a duration

of $8$ hours per day in a shift, however, there is $30$ minutes break in it$.$ There will be one

worker per station. Previous experience suggests that the uptime efficiency for the line will

be $83\%,$ and repositioning time lost per cycle will be $0\mathrm{.}03$min.

Table A:

Requirements:

a$)$ How would you design the Precedence diagram for the above?

b$)$ Determine the cycle time $($Tc$)?$

c$)$ Determine the minimum number of workers required on the line.

d$)$ Determine the service time $($Ts$)$ to which the line must be balanced.

A standard deck of cards is being used to play a game. There are four suits $($hearts$,$ diamonds,

clubs, and spades$),$ each having $13$ faces $($ace$,2,3,4,5,6,7,8,9,10,$ jack, queen, and king$),$

making a total of $52$ cards. This complete deck is thoroughly mixed, and you will receive the

first $2$ cards from the deck without replacement.

a$.$ What is the probability that both cards are kings? $(3$ Marks$)$

b$.$ What is the probability that the first card is a $10$ and the second card is a $6$ or a $7?(3$

Marks$)$