Question

a students is taking five course and is facing the crunch of final exams.she estimates that she has 40 hours available to study .if xj=the number of hours allocated to study for coursej.state the equation whose solution set specifies all possible allocation of time among the five courses which will exhaust the 40 hours

Answer 1

Student has five subjects and 40 hrs available.

So,$x_1+x_2+x_3+x_4+x_5=40$

$0\leq x_1\leq40, \,0\leq x_2\leq40,\\ 0 \leq x_3\leq40,0\leq x_4\leq40,0 \leq x_5\leq40,$

where $x_1,x_2,x_3,x_4,x_5$ are real numbers.

This is the equation whose solution set specifies all possible allocation of time among the five courses which will exhaust the 40 hours.