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
- An organization allows its employees to work independently on consultancy projects but charges an overhead on the consulting fee. The overhead is 20% of the consulting fee, if the fee is up to . 5,00,000. For higher fees, the overhead is . 1,00,000 plus 10% of the amount by which the fee exceeds . 5,00,000. The government charges a Goods and Services Tax of 18% on the total amount (the consulting fee plus the overhead). An employee of the organization charges this entire amount, i.e., the consulting fee, overhead, and tax, to the client. If the client cannot pay more than . 10,00,000, what is the maximum consulting fee that the employee can charge?
Three frictionless pulleys with rope attachment are in a static equilibrium as shown in the figure. The mass $m_1$ and $m_2$, in kg, respectively are
If the in-situ density of coal is 1320 kg/m$^3$ and the density of blasted coal is 952 kg/m$^3$, the swell factor is _____________ (rounded off to 3 decimal places)
A five-member truss system is shown in the figure. The maximum vertical force P in kN that can be applied so that loads on the member CD and BC do NOT exceed 50 kN and 30 kN, respectively is _____________(rounded off to 2 decimal places)
The Fourier transform and its inverse transform are respectively defined as $\tilde{f}(\omega) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(x)e^{i\omega x}dx$ and $f(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} \tilde{f}(\omega)e^{-i\omega x}d\omega$. Consider two functions $f$ and $g$. Another function $f * g$ is defined as
$(f * g)(x) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{+\infty} f(y)g(x - y)dy$
Which of the following relation is/are true?
Note: Tilde ($\sim$) denotes the Fourier transform.
