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Question
The total cost function for production of x articles is given as C = 100 + 600x – 3x2 . Find the values of x for which total cost is decreasing.
Solution
Given, the cost function is
C = 100 + 600x - 3x2
∴ `"dC"/"dx" = 0 + 600 - 6"x"`
= 600 - 6x
= 6(100 - x)
Since total cost C is a decreasing function,
`"dC"/"dx" < 0`
∴ 6(100 - x) < 0
∴ 100 - x < 0
∴ 100 < x
∴ x > 100
∴ The total cost is decreasing for x > 100.
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A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price per item is given as p = 120 – x. Find the value of x for which elasticity of demand for price ₹ 80.
Solution: Total cost C = 40 + 2x and Price p = 120 – x
p = 120 – x
∴ x = 120 – p
Differentiating w.r.t. p,
`("d"x)/("dp")` = `square`
∴ Elasticity of demand is given by η = `- "P"/x*("d"x)/("dp")`
∴ η = `square`
When p = 80, then elasticity of demand η = `square`
Complete the following activity to find MPC, MPS, APC and APS, if the expenditure Ec of a person with income I is given as:
Ec = (0.0003)I2 + (0.075)I2
when I = 1000
If elasticity of demand η = 0 then demand is ______.
In a factory, for production of Q articles, standing charges are ₹500, labour charges are ₹700 and processing charges are 50Q. The price of an article is 1700 - 3Q. Complete the following activity to find the values of Q for which the profit is increasing.
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Then C = standing charges + labour charges + processing charges
∴ C = `square`
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Profit `pi = R - C = square`
Differentiating w.r.t. Q, we get
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If profit is increasing , then `(dpi)/(dQ) >0`
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Hence, profit is increasing for `Q < square`
