<span>12^3 = 1728
and
14^3 = 2744
First, let's reduce the range of numbers to check. The cube root of 1000 is 10 and the cube root of 3000 is 14.4225. So we need to look at the numbers 11, 12, 13, and 14. Not looking at 10 since the question states "BETWEEN 1000 and 3000". Now the only way you're going to get an odd number when multiplying 2 numbers is if both numbers are odd. And since we're looking for perfect cubes, that would imply that we're cubing an even number. So the answers will be
12^3 = 1728
and
14^3 = 2744</span>
Answer:
See explanation
Step-by-step explanation:
You have to graph the system of inequalities presented as
Part A:
1. Draw a dotted line 
(dotted because the sign < is without notion "or equal to"). Select one of two regions by substituting the coordinates of origin into inequality:
Since this inequlity is false, the origin doesn't belong to the shaded region, so you have to shade that part which doesn't contain origin (red part in attached diagram).
2. Draw a solid line 
(solid because the sign ≥ is with notion "or equal to"). Select one of two regions by substituting the coordinates of origin into inequality:
Since this inequlity is true, the origin belongs to the shaded region, so you have to shade that part which contains origin (blue part in attached diagram).
The intersection of these two regions is the solution area.
Part B:
Plot point (-2,-2). Since this point doesn't belong to the solution area, this is not a solution of the system of two inequalities. You can check it mathematically - substitute x=-2 and y=-2 into the system:
Both inequalities are false, so (-2,-2) doesn't belong to the solution area.
It can be represented by this expression: -20+20
Answer:
$180000
Step-by-step explanation:
Let's c be the number of chair and d be the number of desks.
The constraint functions:
- Unit of wood available 4d + 3c <= 2000 or d <= 500 - 0.75c
- Number of chairs being at least twice of desks c >= 2d or d <= 0.5c
c >= 0
d >= 0
The objective function is to maximize the profit function
P (c,d) = 400d + 250c
We draw the 2 constraint functions (500 - 0.75c and 0.5c) on a c-d coordinates (witch c being the horizontal axis and d being the vertical axis) and find the intersection point 0.5c = 500 - 0.75c
1.25c = 500
c = 400 and d = 0.5c = 200 so P(400, 200) = $250*400 + $400*200 = $180,000
The 500 - 0.75c intersect with c-axis at d = 0 and c = 500 / 0.75 = 666 and P(666,0) = 666*250 = $166,500
So based on the available zones in the chart we can conclude that the maximum profit we can get is $180000
