2 Marks Questions

Question 12 Marks

A company manufactures cassettes. Its cost and revenue functions are C(x) = 26,000 + 30x and R(x) = 43x, respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold by the company to realise some profit?

Answer

Cost function: C(x) = 26000 + 30x Revenue function : R(x) = 43x For profit, R(x) > C(x)
⇒ 26000 + 30x < 43x
⇒ 43x - 30x > 26000
⇒ 13x > 26000
⇒ x > 2000
Hence, more than 2000 cassettes must be produced to get profit.

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Question 22 Marks

Solve for x, the inequalities Exercises.
$|\text{x}-1|\leq5,\ |\text{x}|\geq2$

Answer

Given that $|\text{x}-1|\leq5,\ |\text{x}|\geq2$
$\Rightarrow-5\leq\text{x}-1\leq5$
$\Rightarrow4\leq\text{x}\leq6$
And $|\text{x}|\geq2$
$\Rightarrow\text{x}\leq-2$ or $\text{x}\geq2$
$\Rightarrow\text{x}\in(-\infty, -2)\cup({2, \infty})$
On combining (i) and (ii), we get,
$\text{x}\in(-4, -2)\cup({2, 6})$

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Question 32 Marks

Solve for x, the inequalities Exercises.
$\frac{4}{\text{x+1}}\leq3\leq\frac{6}{\text{x+1}}, (\text{x}>0)$

Answer

$\frac{4}{\text{x+1}}\leq3\leq\frac{6}{\text{x+1}}, (\text{x}>0)$
$\frac{4}{\text{x+1}}\leq3$ and $3\leq\frac{6}{\text{x}+1}, \text{x}>0$
$\Rightarrow4\leq3({\text{x+1}})$ and $3({\text{x+1}})\leq6,\text{x}<0$
$\Rightarrow\frac{1}{3}\leq\text{x}$ and $\text{x}\leq1, \text{x}>0$
$\Rightarrow\frac{1}{3}\leq\text{x}\leq1$

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Question 42 Marks

Solve for x, the inequalities Exercises.
$4\text{x}+3\geq2\text{x}+17$

Answer

We have $4\text{x}+3\geq2\text{x}+17$
$\Rightarrow4\text{x}-2\text{x}\geq17-3$
$\Rightarrow2\text{x}\geq14$
$\Rightarrow\text{x}\geq7\ ...(\text{i})$
Also, we have $\text{3x}-5\leq-2$
$\Rightarrow\text{3x}\leq-2+5$
$\Rightarrow\text{3x}\leq3$
$\Rightarrow\text{x}\leq1\ ...(\text{ii})$
From (i) and (ii), no value of x is possible.

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