Answer:
Two mittens and seven gloves
Step-by-step explanation:
I presume you are asking how many mittens and how many gloves Beth should knit to produce the most profit.
Let x = the number of mittens and
Let y = the number of gloves
1. Summarize the information in a table
2. List the constraints
(a) Beth can't make a negative number of mittens, so
x ≥ 0.
(b) Neither can she make a negative number of gloves, so
y ≥ 0.
(c) The total number of minutes on Machine A cannot exceed 32, so
2x + 4y ≤ 32.
(d) The total number of minutes on Machine B cannot exceed 18, so
2x + 2y ≤ 18.
(e) The total number of minutes on Machine C cannot exceed 24, so
4x + y ≤ 24.
3. Write an equation for the profit
P = 8.00x + 10.00y
4. Graph the constraints to identify the feasible region
See the figure below. The feasible region is the dark green area where all three regions overlap.
5. Determine the points of intersection between the constraints
(i) Constraints (c) and (d)
The lines intersect at (2,7).
(ii) Constraints (c) and (e)
The lines intersect at (27/7,32/7).
(iii) Constraints (d) and (e)
The lines intersect at (5,4).
6. Determine the x- and y-intercepts of the feasible region
(i) x-intercept
The x-intercept is at (6,0).
(ii) y-intercept
The y-intercept is at (0,8).
The five black dots are the vertices of the polygon that represents the feasible region.
7. Calculate the maximum profit
Calculate the profit at each of the vertices.
(i) At (0,0)
P = 8.00x + 10.00y = 8.00(0) + 10.00(0) = 0 + 0 = $0
(ii) At (2,7)
P = 8.00(2) + 10.00(7) = 16 + 70 = $86
(iii) At (5,4)
P = 8.00(5) + 10.00(4) = 40 + 40 = $80
(iv) At (6,0)
P = 8.00(6) + 10.00(0) = 48 + 0 = $48
The maximum profit occurs at (2,7)
Thus, Beth should knit two mittens and seven gloves.
Answer:
Choice C is correct
Step-by-step explanation:
The first step is to re-write the equations in exponential form.
The first equation can be written as;
since the base is 10 and 4 the exponent.
The second equation can be written as;
The second step is to make N the subject of the formula in both equations.
Solving for N from this equation , yields;
Solving for N from the second equation , yields;
Therefore;
Answer:
72
Step-by-step explanation:
The area (A) of a rhombus is calculated as
A = × d₁ × d₂ (d₁ and d₂ are the diagonals )
The diagonals bisect each other at right angles
d₁ = 2 × 6 = 12
Use the tangent ration in the upper left right triangle and the exact value
tan60° =
tan60° = =
=
( multiply both sides by 6 )
opp = 6 , then
d₂ = 2 × 6 = 12
Thus
A = × 12 × 12
= 6 × 12
= 72
Answer: Anything between 0 and 10, excluding both endpoints.
In terms of symbols we can say 0 < w < 10 where w is the width.
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Explanation:
You could do this with two variables, but I think it's easier to instead use one variable only. This is because the length is dependent on what you pick for the width.
w = width
2w = twice the width
2w-5 = five less than twice the width = length
So,
which lead to
area = length*width
area = (2w-5)*w
area = 2w^2-5w
area < 150
2w^2 - 5w < 150
2w^2 - 5w - 150 < 0
To solve this inequality, we will solve the equation 2w^2-5w-150 = 0
Use the quadratic formula. Plug in a = 2, b = -5, c = -150
Ignore the negative solution as it makes no sense to have a negative width.
The only practical root is w = 10.
If w = 10 feet, then the area = 2w^2-5w results in 150 square feet.
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Based on that root, we need to try a sample value that is to the left of it.
Let's say we try w = 5.
2w^2 - 5w < 150
2*5^2 - 5*5 < 150
25 < 150 ... which is true
This shows that if 0 < w < 10, then 2w^2-5w < 150 is true.
Now try something to the right of 10. I'll pick w = 15
2w^2 - 5w < 150
2*15^2 - 5*15 < 150
375 < 150 ... which is false
It means w > 10 leads to 2w^2-5w < 150 being false.
Therefore w > 10 isn't allowed if we want 2w^2-5w < 150 to be true.