Foundry Cost Per Tonne Calculation
This problem requires calculating the cost per tonne for a foundry based on its fixed and variable production costs.
Cost Components Analysis
The total cost of production consists of two parts:
- Fixed Daily Cost: Rs 50,000 (This cost is incurred regardless of production volume).
- Variable Cost: Rs $800Q$, where $Q$ is the daily production in tonnes. This cost depends directly on the production quantity.
Calculating Total Production Cost
We need to find the total cost when the daily production ($Q$) is 100 tonnes.
- Calculate the Variable Cost (VC) for $Q = 100$ tonnes:
VC = Rs $800 \times Q$
VC = Rs $800 \times 100 = \text{Rs } 80,000$
- Calculate the Total Cost (TC) by adding the Fixed Cost (FC) and Variable Cost (VC):
TC = FC + VC
TC = \text{Rs } 50,000 + \text{Rs } 80,000 = \text{Rs } 130,000$
Determining Cost Per Tonne
The cost per tonne is calculated by dividing the Total Cost (TC) by the total production ($Q$).
- Calculate the Cost Per Tonne:
Cost per Tonne = \frac{TC}{Q}
Cost per Tonne = \frac{\text{Rs } 130,000}{100 \text{ tonnes}} = \text{Rs } 1300 \text{ per tonne}
The calculated cost of production is Rs 1300 per tonne for a daily production of 100 tonnes. This value falls within the provided range.
Important Questions from Numerical Computation
$A$ is an ($n \times n$) matrix. Consider the following two statements
Statement 1: Columns of matrix $A$ are linearly independent
Statement 2: Inverse of matrix $A$ exists
Which one of the following statements is TRUE?
- Consider the function $G(x, y, z) = 0$. This function allows us to implicitly define each of three variables as a function of the other two variables. Assume that all partial derivatives of the function $G(x, y, z)$ exist everywhere. Then, the value of $\left(\frac{\partial z}{\partial x} \times \frac{\partial x}{\partial y} \times \frac{\partial y}{\partial z}\right)$ is _________ (in integer)
- Levenshtein distance is used to measure the minimum edit distance between two strings by counting the minimum number of editing operations (such as, insertions, deletions, substitutions) required to transform one string to another. Consider an alternative version of the Levenshtein distance in which each insertion and each deletion has a cost of 1 and substitutions are not allowed.
Based on this alternative version, the Levenshtein distance between the strings, word and work is ______ (Answer in integer). - In a given collection of documents, let $N$ be the total number of documents and let $d$ be the number of documents in which the term $t$ occurs.
Which ONE of the following fractions is used to define the inverse document frequency (idf) of the term $t$? - The total number of unique character bigrams in the string thoughtsoftheghosts (which contains 19 characters) is ______.
