In part a, you determined that you can make 40 servings from five packages of buns and four packages of hot dogs without anything left over. this means that you can also make 80, 120, 160, and so forth, servings without anything left over. these numbers are called multiples of 40.you need to find the smallest integer multiple of 40 that is greater than or equal to 700. then, use this to determine the number of packages of buns and hot dogs.

ceiling(700/40) = ceiling(17.5) = 18 . . . . ceiling(x) is the smallest integer ≥ x.

The smallest integer multiple of 40 that is larger than 700 is 18.

The number of packages of buns will be 18*5 = 90.

The number of packages of hotdogs will be 18*4 = 72.

These numbers will ensure that you have 20 bun/hotdog combinations left over. If you want to minimize leftovers, you would use 88 packages of buns and 70 packages of hotdogs. That would give you 4 buns and no hotdogs left over.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be