Vishal and Sam are running a business. They invested Rs 5000 as a fixed cost. Their variable cost is given by the function $x^{2} - 100 x + 1000$ What is the least number of units they must sell at Rs 100 to earn a profit of Rs 1500?

50 units

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100 units

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150 units

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200 units

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Solution

The correct option is A
50 units

$T C = T F C + T V C 5000 + x^{2} - 100 x + 1000 T R = 100 x Π = T R - T C = 200 x - x^{2} - 6000$

Given that profit is Rs 1500
$\Rightarrow 200 x - x^{2} - 6000 = 1500 \Rightarrow x^{2} - 200 x + 7500 = 0 (x - 150) (x - 50) = 0 x = 150 o r x = 50$

The minimum output level corresponding to a profit of Rs 1500 is 50 units

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Vishal and Sam are running a business. They invested Rs 5000 as a fixed cost. Their variable cost is given by the function x2−100x+1000 What is the least number of units they must sell at Rs 100 to earn a profit of Rs 1500?

The correct option is A 50 units TC=TFC+TVC5000+x2−100x+1000TR=100xΠ=TR−TC=200x−x2−6000 Given that profit is Rs 1500 ⇒200x−x2−6000=1500⇒x2−200x+7500=0(x−150)(x−50)=0x=150 or x=50 The minimum output level corresponding to a profit of Rs 1500 is 50 units

Vishal and Sam are running a business. They invested Rs 5000 as a fixed cost. Their variable cost is given by the function $x^{2} - 100 x + 1000$ What is the least number of units they must sell at Rs 100 to earn a profit of Rs 1500?