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 $(V+F)$?

• 5
• 4
• 7
• 6

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

• 5
• 10
• 15
• 25

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

• 748

• 873

• 953

• 1148

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.

• Answer

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 $ $500+0.2N^{1.3}$. 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 _____

• Answer

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: $$C_T=100f_1+\frac{1000}{f_1{f}_2}+20f_2^2+50$$ The lowest total cost $C_T$, in millions of dollars (up to one decimal place), is ____________

• Answer

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 _________

• Answer

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

• order 200 frames every time
• accept 2% discount
• accept 4% discount
• order Economic Order Quantity

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)

• remains the same
• gets halved
• gets doubled
• becomes four times