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Process Economics - GATE-CH Questions

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## Economic Design

### GATE-CH-2011-61-eco-2mark

The variable cost (

\(V\)) of manufacturing a product varies according to the equation

\(V=4q\), where

\(q\) is the quantity produced. The fixed cost (

\(F\)) of production of same product reduces with

\(q\) according to the equation

\(F=100/q\). How many
units should be produced to minimize the total cost

\((V+F)\)?

### GATE-CH-2012-58-eco-2mark

The cost function for a product in a firm is given by

\(5q^2\), where

\(q\) is the amount of production. The firm can sell the product at a market price of 50 per unit. The number of units to be produced by the firm such that the profit is maximized is

### GATE-CH-2012-43-eco-2mark

A batch reactor produces \(1\times 10^5\) kg of a product per year. The total batch time (in hours) of the reactor is \(k\sqrt {P_B}\), where \(P_B\) is the product per batch in kg and \(k=1.0\) h/\(\sqrt {\text {kg}}\). The operating cost of the reactor
is $ 200/h. The total annual fixed charges are $ \(340\times P_B\) and the annual raw material cost is $ \(2\times 10^6\). The optimum size (in kg) of each batch (adjusted to the nearest integer) is

### GATE-CH-1998-27-eco-5mark

Capital cost of a pipeline of exotic material is estimated as \(3D^{1.5}\) Rs./m. where \(D\) is the pipe diameter in mm. The annual maintenance cost is estimated as 10% of the total capital cost. Annual operating cost of the pipe is given as follows:
\[ \text {Annual operating cost } = 3 \times 10^{15}/D^5 \text { Rs./(m.year)} \] Estimate the most economic pipe diameter (in mm) based on the least annual cost approach to the nearest multiple of 10 mm. Estimated amortization period is 10 years.

### GATE-CH-2013-47-eco-2mark

A plant manufactures compressors at the rate of

\(N\) units/day. The daily fixed charges are $ 20000 and the variable cost per compressor is $

\(500 + 0.2 N^{1.3}\). The selling price per compressor is $ 1000. The number of compressors to be manufactured,
to the nearest integer, in order to maximize the daily profit is _____

[Index]

### GATE-CH-2015-53-eco-2mark

The cost of two independent process variables \(f_1\) and \(f_2\) affects the total cost \(C_T\) (in millions of dollars) of the process as per the following function: \[ C_T = 100 f_1 + \frac {1000}{f_1f_2} + 20f_2^2+50 \] The lowest total cost \(C_T\),
in millions of dollars (up to one decimal place), is ____________

### GATE-CH-2017-54-eco-2mark

The total cost (

\(C_T\)) of an equipment in terms of the operating variables

\(x\) and

\(y\) is

\[ C_T = 2x + \frac{12000}{xy} + y + 5 \] The optimal value of

\(C_T\), rounded to 1 decimal place, is _________

### GATE-CH-ME-2010-46-eco-2mark

Annual demand for window frames is 10000. Each frame costs $ 200 and ordering cost is $ 300 per order. Inventory holding cost is $ 40 per frame per year. The supplier is willing to offer 2% discount if the order quantity is 1000 or more, and 4% if the
order quantity is 2000 or more. If the total cost is to be minimized, the retailer should

### GATE-CH-PI-2010-42-eco-2mark

If annual demand, ordering cost and carrying cost become four times of their respective original values, then the economic order quantity (EOQ)

[Index]

Last Modified on: 02-May-2024

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