A business is using 'Moving Averages$-4\text{'}($MA$-4)$ forecasts to decide production quantities. The production manager is complaining that the production quantities significantly vary from period to period, making it difficult to manage the capacity.

What will be your suggestion in this situation?

Answer clearly in one sentence.

$[1\mathrm{.}5$ marks$]$

$2$: A company that produces pleasure boats has decided to expand one of its lines. The current facility is insufficient to handle the increased workload, so the company is considering two expansion alternatives.

With Option A$,$ the annual fixed cost will be $$50,000,$ energy cost will be $$200$ per boat, labour cost will be $$500$ per boat, and material cost will be $$600$ per boat. Option B will have an annual fixed cost of $$75,000$ and will result in an energy cost of $$300$ per boat. Option B is$,$ however, more efficient in terms of labour and material. With Option B$,$ the labour cost per boat will be $$400$ and the material cost per boat will be $$500.$

Find the range of annual output for which Option A should be preferred. $[2$ Marks$]$

$3.$ If the trend line equation fitted to $4$ years of annual demand is y $=-9\mathrm{.}4$x$+245\mathrm{.}5,$ and the seasonal relatives $($SR$)$ for the

quarters are: Quarter $1$ SR $=0\mathrm{.}8,$ Quarter $2$ SR $=1\mathrm{.}3,$ Quarter $3$ SR $=1\mathrm{.}2,$ Quarter $4$ SR $=0\mathrm{.}7,$ what is the Quarter $3$ forecast for

the next year? $($Keep $2$ decimal places in your answer.$)[2$ Marks$]$

$4.$ A production system has $4$ workstations in a sequence. The $1$s workstation requires $4$ minutes to complete its tasks to process a unit. The $2$nd and $3$rd workstations require $2\mathrm{.}5$ minutes each to complete their tasks on one unit. The $4$th workstation requires $2$ minutes to complete its tasks on one unit. What is the production rate of this system per hour $($i$.$e$.,$ the number of units produced per hour$)$ considering that the system has been working continuously? $[2$ Marks$]$

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