The maximum value of $\mathrm{\mu }$ = 3x + 4y, subject to the conditions x + y $\le$ 40, x + 2y $\le$ 60, x, y $\ge$ 0, is

• 130

• 140

• 40

• 120

If x + y $\le$ 2; x $\ge$ 20, y $\ge$ 20, then the point, at which the maximumvalue of 3x + 2y is attained, will be

• (0, 0)

• $\left(\frac{1}{2}, \frac{{\displaystyle 1}}{{\displaystyle 2}}\right)$

• (2, 0)

• (0, 2)

The maximum value of P = 6x + 8y, if 2x + y $\le$ 30, x + 2y $\le$ 24; x $\ge$ 20, y $\ge$ 20, will be

• 90

• 120

• 96

• 240

Regression of saving (s) of a family on income y may be expressed as s = a + $\frac{\mathrm{y}}{\mathrm{m}}$, where a and m are constants. In a random sample of 100 families the variance of savings is one quarter of the variance of incomes and the correlation coefficient is found to be 0.8, the value of m is

• 0.8

• 1.25

• 0.25

• None of these