Business. Jack makes $3 profit selling hotdogs and $2 profit selling burgers. Jack wants to earn at least $30 per day. Jack also wants to sell at least 4 burgers and at least 4 hotdogs per day.

Answer 1

3H + 2B > 30

B, H > 4

3(4) + 2B > 30

2B > 18

B > 9 He needs to sell at least 9 burgers, if he only sells 4 hot dogs

3H + 2(4) > 30

3H > 22

H > 7 1/3 He needs to sell at least 8 hot dogs if he only sells 4 burgers

He needs to sell at least as much as one of the following combinations

Hot dogs Burgers

4 9 the point (4,9)

5 8 the point (4,8)

6 6 the point (6,6)

7 5 the point (7,5)

8 3 to get at least 30, but he has to sell at least 4

8 4 the point (8,4)

9 2 to get at least 30, but he has to sell at least 4

9 4 the point (9,4)

plot (4,9) and (6,6) on a graph, H on the horizontal axis, B on the vertical axis

draw a straight line through them.

draw a vertical line at H=4 and a horizontal line at B =4

the feasible points are the area to the right of H=4, above B=4 and to the northeast of the line connecting (4,9) (6,6) or (7 1/3, 4) make the line segment from (4,9) to (7 1/3, 4) dotted, and shade in the area to the north, northwest and west of it. That's the solution set area, although you want only the integer combinations of H and B, so it's a series of endless dots to the north, northeast and east of that line segment including the above combinations in the chart above