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In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the…
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed.
(i)[1.0]
A company sells hand towels at ₹ 100 per unit. The fixed cost for the company to manufacture hand towels is ₹ 35,000 and variable cost is estimated to be 30% of total revenue. What will be the total cost function for manufacturing hand towels?
- (a)$35000 + 3x$
- (b)$35000 + 30x$
- (c)$35000 + 100x$
- (d)$35000 + 10x$
(ii)[1.0]
If the correlation coefficient of two sets of variables $(X, Y)$ is $-\frac{3}{4}$, which one of the following statements is true for the same set of variables?
- (a)Only one of the two regression lines has a negative coefficient.
- (b)Both regression coefficients are positive.
- (c)Both regression coefficients are negative.
- (d)One of the lines of regression is parallel to the x-axis.
(iii)[1.0]
If the total cost function is given by $C = x + 2x^3 - \frac{7}{2}x^2$, find the Marginal Average Cost function (MAC).
(iv)[1.0]
The equations of two lines of regression are $4x + 3y + 7 = 0$ and $3x + 4y + 8 = 0$. Find the mean value of $x$ and $y$.
(v)[1.0]
The manufacturer of a pen fixes its selling price at ₹ 45, and the cost function is $C(x) = 30x + 240$. The manufacturer will begin to earn profit if he sells more than 16 pens. Why? Give one reason.
Answer
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From ISC 2024 Mathematics Paper 1, question 19.