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$)$