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Linear Programming

Multiple Choice Questions

81.

The maximum value of $μ$ = 3x + 4y, subject to the conditions x + y $\leq$ 40, x + 2y $\leq$ 60, x, y $\geq$ 0, is

82.

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

(0, 0)
$(\frac{1}{2}, \frac{1}{2})$
(2, 0)
(0, 2)

83.

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

84.
Regression of saving (s) of a family on income y may be expressed as s = a + $\frac{y}{m}$ , 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

None of these

$Given, s = a + \frac{y}{m}, {σ_{s}}^{2} = \frac{1}{4} {σ_{y}}^{2} and r = 0.8 ∴ s = a + \frac{y}{m} Now, s - s = \frac{1}{m} (y - y) . . . (i) \Rightarrow \sum (s - s) (y - y) = \frac{1}{m} \sum {(y - y)}^{2} \Rightarrow cov (s, y) = \frac{1}{m} {σ_{y}}^{2} . . . (ii) Since, r = \frac{cov (s, y)}{σ_{s} σ_{y}} ∴ 0.8 = \frac{\frac{1}{m} {σ_{y}}^{2}}{σ_{s} σ_{y}} \Rightarrow 0.8 = \frac{1}{m} . \frac{σ_{y}}{σ_{s}} \Rightarrow 0.4 = \frac{1}{m} [∵ σ_{s} = \frac{1}{2} σ_{y}] \Rightarrow m = 2.5$