Nguyens New Years resolution was to lose weight At the begin

Nguyen\'s New Year\'s resolution was to lose weight At the beginning of the New Year, Nguyen weighed 314 pounds. After 128 days, she weighed 218 pounds. Find the rate of change of weight loss over time. Write a linear equation modeling Nguyen\'s weight loss. A printing company ships x copies of BHCC\'s student handbook to the Charlestown campus and y copies to the Chelsea campus. The company must ship a total of at least 240 copies to these two locations. Express this relationship as an inequality. Graph this inequality.

Solution

17)
In the beginning the weight was 314 pounds and at the end of 128 days it became 218 pounds so a loss of =314-216=94 pounds in 128 days so each day 94/128 (= 0.75 ) pound of weight loss
Thus rate of change of weight loss = 0.75 pounds per day (since it is loss the negative value has been factored in)

Lieanr equation => y= mx+c so w_t= 314 -0.75*t where w_t is the weight in pouns on day \'t\' ;


18) \'x\'copies to Charlestown campus and \'y\' copies to Chelsea campus; Total of at least 240 copies to be shipped to these two locations;
Thus in ineqaulity at least means >= sign;
Hence we write the inequality as x+y >= 240;

Now, since this is a straight line with slope = -1; it will cut x axis at (240,0) and y -axis at (0,240) and has a straight line. This is the line, It divides Quadrant 1 into two segements; First is a finite segment bounded by the line and the axis towards the origin (which isn\'t the feasible region) the other is an infinite region above this line and away from the origin, but sitll in the 1st quadrant as x and y cannot be negative;

Thus it is an unbounded region away from the origin and above the line x+y=240 represented by x+y>=240;