<span>Constraints (in slope-intercept form)
x≥0,
y≥0,
y≤1/3x+3,
y</span>≤ 5 - x
The vertices are the points of intersection between the constraints, or the outer bounds of the area that agrees with the constraints.
We know that x≥0 and y≥0, so there is one vertex at (0,0)
We find the other vertex on the y-axis, plug in 0 for x in the function:
y <span>≤ 1/3x+3
y </span><span>≤1/3(0)+3
y = 3.
There is another vertex at (0,3)
Find where the 2 inequalities intersect by setting them equal to each other
(1/3x+3) = 5-x Simplify Simplify Simplify
x = 3/2
Plugging in 3/2 into y = 5-x: 10/2 - 3/2 = 7/2
y=7/2
There is another vertex at (3/2, 7/2)
There is a final vertex where the line y=5-x crosses the x axis:
0 = 5 -x , x = 5
The final vertex is at point (5, 0)
Therefore, the vertices are:
(0,0), (0,3), (3/2, 7/2), (5, 0)
We want to maximize C = 6x - 4y.
Of all the vertices, we want the one with the largest x and smallest y. We might have to plug in a few to see which gives the greatest C value, but in this case, it's not necessary.
The point (5,0) has the largest x value of all vertices and lowest y value.
Maximum of the function:
C = 6(5) - 4(0)
C = 30</span>
Answer:
Inconsistent
Step-by-step explanation:
We are given the equations;
0.3y=0.6x+0.3
1.2x+0.6=0.6y
Assuming we are required to determine whether the system of equations are consistent or inconsistent
We are going to use substitution
Making y the subject;
Equation 1: 0.3y=0.6x+0.3
Dividing both sides by 0.3
y = 2x + 1
Equation 2: 1.2x+0.6=0.6y
Dividing both sides by 0.6
y = 2x + 1
This means both equations are similar and we can't get a solution.
Therefore, the system of equations is inconsistent.
Answer:
c) 14/5 = 2.8 each (better value)
Step-by-step explanation:
a) 9/3 = 3 each
b) 28/7 = 4 each
c) 14/5 = 2.8 each (better value)
Answer:
23/100 or 23/10
Step-by-step explanation:
2.3/1
(2.3 x 10) / (1 x 10) =23/10
find lcm (lowest common multiple) for 23 and 10
1 is the lcm for 23 and 10
23/10 is a simplest fraction for the decimal point number 2.3
9514 1404 393
Answer:
Step-by-step explanation:
The difference in ages remains the same over time. Enoch, at twice Martin's age, is still 15 years older. That means Martin is 15 and Enoch is 30.
