Please solve using inventory build up diagram.

Imentory buildup diagram with

initial given setuy, where

wheat comes in at $40,000ggh$

proused at $20,000ygh.$

$(1)$ In this, the bim will

get filled at $1100ms.$

At $11$;$00hrs$ the bim will be full & they have to wait

twel the bion is mpptied. This wile take another $4$ hrrs e by

that time fames will veturn i$.$e$.150$ obrs.

$(3)$ Max. time which $4$ farmer hes to $w$ ait is $=1.4$hmos to $150$mos

In coming trmk rate $=\frac{40,000}{4000}=10$ truks $\frac{?}{ln}.$

$(5)$ Writigy wost $=1\mathrm{.}25801,000=*1,00,000$ If we add procesing capait, by $10,000l\frac{y}{h}r.$

If we ald processing coparit, by prousing time

Since rejular shift is only till $1700$ trs$.$

$O.O.T.wht=\frac{110}{60}300=b,2000$

But im this care full wheat will be consuoned Noit y

time for

trudes. cost$=R_{5}8100,$cdots$=B_5*800000$

overtime $=2300-1700=6hms.$

$OT$ wost $=63000=18018,000$

:$.$ Tofel Add. $=$ wot $=Bs818,000$

& No waitigy wst for tractors & fuel wstis ation

of wheat so ket so left ovor semains hese.

$(04)$

So adding bins $(8$ No$.$S$)$ is less costly then

imcrearing procesingity by $10,000$ ly$/$mill

$7\mathrm{.}25+07$ torto$4=\frac{26\mathrm{.}25}{40}$ Solve numerical questionNumerical Question

Wheat Procurement and Processing at XYZ Company Limited $(10$ Marks$)$

XYZ Company procures and processes wheat. During the wheat harvest season, farmers $($using their

tractors$)$ bring wheat from the fields to the processing plant during $0700-1500hrs.$ On peak days,

approximately $40,000kg$ of wheat is brought in per hour. Tractors dump their contents in holding

bins silos in the storage area. XYZ has bins to hold $80,000kg$ of wheat. When bins are full, incoming

tractors must wait for unloading. A conveyor belt moves wheat from the bins to the processing plant.

The wheat is processed at the rate of $20,000kg/$hour$.$ The regular shift at the plant is for $10$ hours

starting at $0700$ hrs$.$

Assuming that wheat arrives continuously over time, construct an inventory build$-$up diagram$($s$)$

for the storage area at XYZ$.(2$ marks$)$

Assuming, finally, that each vehicle can accommodate about $4,000kg$ of wheat, at what point

during the day must tractors begin waiting before unloading into the storage bin? $(1$ mark$)$

What is the maximum amount of time that a tractor must wait? $(1$ mark$)$

How long will tractors wait on average? $(1$ mark$)$

$xYZ$ is concerned about the long waiting hours for farmers and the overtime costs in their plant.

The labor cost during regular time is Rs$.\frac{2000}{hr}$ whereas it is Rs$.3000$ hr during overtime. XYZ

has estimated that the economic cost of waiting is Rs$.\frac{1000}{hr}$ tractor. They have a policy of not

carrying the collected wheat to the next day i$.$e$.$ they insist on same day processing. To overcome

the problems faced, they are contemplating either $($a$)$ to add storage capacity, or $($b$)$ to add

processing capacity. The storage bins are available in the capacity of $10,000kg$ and cost Rs$.$

$100,000$ each. The wheat processing capacity too can be enhanced in the form of $10,000\frac{kg}{hr}$

processors but will cost Rs$.1,000,000$ for the each. What should XYZ do$?(5$ marks$)$