A manufacturer produces two types of products, $$1$$ and $$2,$$ at production levels of $${x_1}$$ and $${x_2}$$ respectively. The profit is given is$$2{x_1} + 5{x_2}.$$ The production constraints are $$$\eqalign{ & {x_1} + 3{x_2} \le 40 \cr & 3{x_1} + {x_2} \le 24 \cr & {x_1} + {x_2} \le 10 \cr & {x_1} > 0,\,{x_2} > 0 \cr} $$$

The maximum profit which can meet the constraints is

In terms of theoretical stress concentration factor $$\left( {{k_t}} \right)$$ and fatigue stress concentration factor $$\left( {{k_f}} \right),$$ the notch sensitivity $$'q'$$ is expressed as

The $$S$$-$$N$$ curve for steel becomes asymptotic nearly at

In a band brake the ratio of tight side band tension to the tension on the slack side is $$3.$$ If the angle of overlap of band on the drum is $${180^ \circ }$$ the coefficient of friction required between drum and the band is