Answers
The combination that gives the most profit exists 12nVIP rings and 12 SST rings (900 day).
What is meant by linear programming?When a linear function is exposed to various constraints, it is maximized or reduced using the mathematical modeling technique known as linear programming. In commercial planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
This is a linear programming problem.
The objective function is profit R, which has to be maximized.
R = 40 V + 35 S
being V: number of VIP rings produced, and S: number of SST rings produced.
The restrictions are
Amount of rings (less or equal than 24 a day):
V + S ≤ 24
Amount of man-hours (up to 60 man-hours per day):
3 V + 2 S ≤ 60
The number of rings of each type is a positive integer:
V, S ≥ 0
This restrictions can be graphed and then limit the feasible region. The graph is attached.
In which 2 of the restrictions are saturated. In one of these three points lies the combination of V and S that maximizes profit.
The points and the values for the profit function in that point are:
Point 1: V = 0 and S = 24
R = 40 V + 35 S = 40 × 0+35 × 24 = 0 + 840
R = 840
Point 2: V = 12 and S = 12
R = 40 V + 35 S = 40 × 12 + 35 × 12 = 480 + 420
R = 900
Point 3: V = 20 and S = 0
R = 40 V + 35 S = 40 × 20+35 × 0 = 800 + 0
R = 800
The combination that gives the most profit is 12nVIP rings and 12 SST rings (900 day).
The complete question is:
The Acme Class Ring Company designs and sells two types of rings: the VIP and the SST. They can produce up to 24 rings each day using up to 60 total man-hours of labor. It takes 3 man-hours to make one VIP ring, versus 2 man-hours to make one SST ring. How many of each type of ring should be made daily to maximize the company's profit, if the profit on a VIP ring is $40 and on an SST ring is $35?
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Related Questions
GARDENING Molly's school is planning a school-based community garden with the diagram shownIf the school has 64 yards of fencing for the rectangular garden, use a system of equations and a graphing calculator to find the value of Then find the dimensions of the garden.
Answers
The value of x is 5 yards and the length and width of the garden is 20 yards and 12 yards respectively.
Given, the school has 64 yards of fencing for the rectangular garden.
we know that, the perimeter of the rectangle is the sum of twice the length and twice the width.
length (l) = x²-5
width (w) = 4x-8
therefore, 2(l+w) = 64
⇒ 2(x²-5+4x-8) = 64
⇒ 2(x²+4x-13) = 64
⇒ 2x²+8x-26 = 64
⇒2x²+8x-26-64 = 0
⇒2x²+8x-90 = 0
divide the equation by 2.
⇒ x²+4x-45=0
⇒ x²+9x-5x-45 = 0
⇒ x(x+9) - 5(x+9) = 0
⇒ (x+9) (x-5)
⇒ x = -9 or x = 5
therefore, x cannot be negative,
hence x = 5 yards.
therefore, l = x²-5
l = 5² - 5
l = 25-5
l = 20 yards.
w = 4x-8
w = 4(5) - 8
w = 20-8
w = 12 yards.
Hence we get the value of x as 5 yards and the dimensions of the garden as 20 yards by 12 yards,
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Factor 3z^2(8z^2-14z+3)
Answers
Answer:
3z²(4z-1)(2z-3)
Step-by-step explanation:
Factor 8z²-14z+3
8z²-14z+3 = (4z-1)(2z-3)
So 3z² (8z²-14z+3)
= 3z²(4z-1)(2z-3)
Hello! Vectors u and v are shown in the graph. What is -3(u x v)?
Answers
Explanation
The values of the vectors are shown below
Thus
[tex]\begin{gathered} u=(6,5) \\ v=(-6,-10) \end{gathered}[/tex]Thus to get -3(u.v) will be
[tex]\begin{gathered} step\text{ 1} \\ find\text{ the dot product} \\ u.v=6(-6)+5(-10) \\ u.v=-36-50 \\ u.v=-86 \end{gathered}[/tex]The next step will be
[tex]\begin{gathered} -3(u.v)=-3\times-86=258 \\ \\ -3(u.v)=258 \end{gathered}[/tex]The answer will be
An automobile travels 415 miles on 16 2/3 gallons of gasoline.
a) How many miles per gallon does the car get on the trip? (Enter your answer as a simplified mixed number.)
b) How many gallons would be required for the car to travel 498 miles?
Answers
B. 20 gallons
Can anyone answer this question fast?
Answers
Sauce = 15
15/3 = 5
Cheese = 12
12/3 = 4
To make 1 pizza you need 5 sauce and 4 cheese.
Multiply these ingredients by 7 to make 7 pizzas:
5*7 = 35
4*7 = 28
You need 35 sauce and 28 cheese
Choose the correct ordering of the numbers below from greatest to least.L. 779.56M. 29.7023N. 7.8695O. 0.8436P. 70.7540
Answers
When you order a number, you must check the number most in the left. The number L and the number M for example,
L. 779.56
M. 029.7023
In the hundreds place, L has a '7', and M has a '0', this means L is bigger than M.
Doing the same procedure with the other, we get the following order:
[tex]\begin{gathered} 779.56>70.7540>29.7023>7.8695>0.8436 \\ L>P>M>N>O \end{gathered}[/tex]What is the range shown in the graph below ?
Answers
Take into account that the range are all availables values of the function, that is, available values of the y coordinate in the graph.
As you can notice, such values are in the following interval:
range: (-∞,8]
XZ¯¯¯¯¯¯¯¯ has a point Y between points X and Z. XY=17, YZ=4x+9, and XZ=11x−9.
Answers
Applying the segment addition postulate, the value of x = 5.
What is the Segment Addition Postulate?According to the segment addition postulate, if three lines, X, Y, and Z are collinear points, that is they lie on a straight line such that Y is between points X and Z, then the sum of the lengths of segments XY and YZ would be equal to the length of segment XZ.
Therefore:
XY + YZ = XZ [segment addition postulate]
Given:
XY = 17
YZ = 4x + 9
XZ = 11x − 9.
Substitute
17 + 4x + 9 = 11x - 9
26 + 4x = 11x - 9
26 + 9 = 11x - 4x
35 = 7x
35/7 = x
x = 5
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A right isosceles triangle has an area of 40.5 cm2. How tall is it?
Answers
Area = 40 cm^2
base = ?
height = x
Area = base * height / 2
bh = 2(40.5)
bh = 81 cm^2
81 3
27 3
9 3
3 3 height = 3 x3 x 3 base = 3
1
The height must be 27 cm and the base 3 cm.
At the end of a party, 3/4 cup of smoked fish dip is left. Jim divides 4/5 of the leftover smoked fish dip equally between 2 friends. How much dip does each friend get?
Answers
Each friend gets 3/10 or 0.3 dips if, at the end of a party, 3/4 cup of smoked fish dip is left.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
Let each freind get x part.
The 3/4 part dipped:
The value of x can be found as follows:
x = (3/4)(4/5) ÷ 2
x = 3/(5×2)
x = 3/10
x = 0.3
Thus, each friend gets 3/10 or 0.3 dips if, at the end of a party, 3/4 cup of smoked fish dip is left.
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Find the intersection points of f(x) = (x + 7)(x - 5) and g(x) = x-5.
510
Answers
Answer:
-7
Step-by-step explanation:
all answers are in the picture
Evaluate the expression when m = -4. M^2+6m+9
Answers
The answer is 1
I believe the answer to be 0.15 but I just want to make sureSuppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.57 and a standard deviation of 0.44. Using the empirical rule, what percentage of the students have grade point averages that are greater than 3.89? Please do not round your answer
Answers
First, we need to find the z-score for the measure x=3.89. This is given by
[tex]z=\frac{x-\mu}{\sigma}=\frac{3.89-2.57}{0.44}[/tex]which gives
[tex]z=3[/tex]Now, from the empirical rule :
we can see that
[tex]P(x>3.89)=P(z>3)\approx0.15\text{ \%}[/tex]Then, the answer is 0.15%
An equality that represents numbers that are not a solution of x-1.2>2.8
Answers
The solution is x> 4 or x ∈(4,∞)
Here equality given is
x - 1.2> 2.8
Rearrange the variable to the left side of the equation
x > 2.8 + 1.2
Calculate the sum
x > 4
Or we can also say
x ∈ (4,∞)
Therefore the range of x is x∈ (4,∞).
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how do i do square root of 24 on the simplified radical form
Answers
Re-write the question as :
[tex]\sqrt{24}[/tex]This can further be written using factors of 24 as;
[tex]\sqrt{6\ast4}[/tex]Separate as :
Put the correct number in each box 1/7 = 4/? = ?/56
Answers
Answer: 1/7 = 4/28 = 8/56
Step-by-step explanation: 7 timestables
Answer:
1/7=4/28=8/56
Step-by-step explanation:
From the pattern of the question we can see that the numerator of the second fraction is 4 and the previous fraction's numerator is 1 that means the fraction has been multiplied by 4. Therefore multiplying the numerator and denominator results in the answer 4/28. For the last fraction we can see that the denominator is 56 and is the double of 28 therefore doubling the whole second fraction we get our answer as 8/56. Overall equating all the three fractions we get the same answer 1/7 after minimizing the fraction.
Username: TNakashrai
I only need help with the gauss elimination and back substitution, and cramers rule. I know hwo to do everything else.
Answers
To solve the equation by Gauss elimination method first convert the equation in matrix form.
The cramers rule is as follows;
The Whistling Straits Corporation needs to raise $40 million to finance its expansion intonew markets. The company will sell new shares of equity via a general cash offering toraise the needed funds. If the offer price is $35 per share and the company'sunderwriters charge a 11 percent spread, how many shares need to be sold?
Answers
Solution
Explanation:
Total Finance Needed = $40,000,000
Offer price per share = $35 per share
Charges of underwriter = 11%
Total Number of shares needed to be sold = ( $40,000,000 / $35 ) x 111%
Total Number of shares needed to be sold = 1,142,857 x 111%
Total Number of shares needed to be sold = 1,267,571 shares
The Whistling Straits Corporation needs 1,267,571 shares to raise $40 million
Evaluate. 0⁴= please
Answers
y + 3 = 2/5(x + 5) , put that into standard form
Answers
Given:
[tex]y+3=\frac{2}{5}(x+5)[/tex]The standard form of the linear equation is,
[tex]Ax+By=C[/tex]Simplify the given equation,
[tex]\begin{gathered} y+3=\frac{2}{5}(x+5) \\ 5(y+3)=2(x+5) \\ 5y+15=2x+10 \\ 2x-5y=15-10 \\ 2x-5y=5 \end{gathered}[/tex]Answer: Standard form is 2x - 5y = 5
5/6x-2/3(x-2) + 1/2 please helppp
Answers
Answer:38
Step-by-step explanation:
MapsQuestion 120 ptsIf a recipe calls for 58 ounces of pecans andthere are 16 ounces in 2 cups, how many pecanswill you need?
Answers
the recipe needed = 58 ounces of pecans
we have 16 ounces in 2 cups,
so we need
58 - 16 = 42 ounces
so we need 42 ounces of pecans.
What is the answer with a posible fraction remainder3.8/21.85
Answers
The solution with a potential fraction remainder for the given fraction, 3.8/21.85, is 0.
How to find the remainder?By shifting the decimal point 1 places to the right, you can convert the divisor 3.8 to a whole number. Then, move the decimal point in the dividend by one place to the right, keeping the same position.
what do you understand by remainder ?The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.
These equations follow:
218.5 ÷ 38 = 5.750
because of this:
21.85 ÷ 3.8 = 5.750
To three decimal places, both calculations.
0 0 5. 7 5 0
3 8 √2 1 8. 5 0 0
− 0
2 1
− 0
2 1 8
− 1 9 0
2 8 5
− 2 6 6
1 9 0
− 1 9 0
0 0
− 0
0
The answer is 0.
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10 Caleb divides powers of 10 using exponents . He says that 0.6 divided by increases the value of the 6. Do you agree with Caleb ? 10 ^ 2 Explain your thinking
Answers
I disagree with Caleb because the value decreased after the quotients are carried out
How to determine the true statement?From the question, the statement is given as
He says that 0.6 divided by 10² increases the value of the 6.
The mathematical expression of the above statement is represented as
0.6 divided by 10²
So, we have
0.6/10²
When the above quotient is evaluated, we have
0.6/10² = 0.006
The above result is different from Caleb's reasoning
This is so because 0.6 divided by 10² decreases the value of the 0.006, instead of increasing the value to 6, as stated by Caleb
Hence, Caleb's reasoning is incorrect
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Complete question
Caleb divides powers of 10 using exponents. He says that 0.6 divided by 10² increases the value of the 6.
Do you agree with Caleb? Explain your thinking
Complete Complete the following tick -tac-toe board to find the three in a row there is only one correct way to make the tick-tac-toe, three in row! The code to unlock the puzzle will be the product of the three the following three puzzle Tic tac toe
Answers
the rest of the question say find the length of the whole secant of the bottom
Answers
According to the Intersecting Secants Theorem,
[tex]\begin{gathered} x\times6=(12+8)\times8 \\ 6x=20\times8 \\ x=\frac{80}{3} \\ x=26.\bar{66} \\ x\approx26.67 \end{gathered}[/tex]Thus, the first option is the correct choice.
Percents are the result of expressing numbers as a part of
Answers
Answer:
percentage of fractions
A college student realized that he was spending too much money on music. For the remaining 5 months of the year his goal is to spend a mean of $50 a month towardsmusic. How much can he spend in December, taking into consideration that in the other 4 months he spent $20, $70, S30, and $85, respectively? Round your answerto two decimal places. If necessary
Answers
The mean is given by the sum of all the months divided by the number of months.
Then:
Let's set x for the spending money for December.
There are 5 months.
Hence:
[tex]\operatorname{mean}=\frac{20+70+30+85+x}{5}[/tex]We need to have a mean equal to $50. Set mean = 50.
[tex]50=\frac{20+70+30+85+x}{5}[/tex]Solve for x:
[tex]\begin{gathered} 50=\frac{20+70+30+85+x}{5} \\ 50=\frac{205+x}{5} \\ 5\cdot50=205+x \\ 250=205+x \\ \text{Therefore:} \\ x=250-205 \\ x=45 \end{gathered}[/tex]Hence, If the student wants to complete his goal, he will need to spend $45 in December.
Write a quadratic function in standard form, with a leading coefficient of 1, given x-intercepts 7 and 10. Use "y" as the dependent variable
and "x" as the independent variable.
Answers
Standard form of quadratic function with leading coefficient 1,
x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
As given in the question,
Given :
y is the dependent variable of the required quadratic function.
x is the independent variable of the required quadratic function.
Leading coefficient of quadratic function is 1
X-intercept of the required function is 7 and 10
Standard form of required quadratic function is equal to
y = k (x-a)(x -b)
Here k=1 , a=7 , b=10
y = 1 (x -7)(x - 10)
⇒ y = x² -7x -10x +70
⇒ y= x² -17x +70
Therefore, standard form of quadratic function with leading coefficient 1, x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
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Does the equation y-250x=500 represent the same relationship between the distance from the start of the trail and the elevation? Explain your reasoning pls
Answers
The equation of a line with slope m and y-intercept b is:
[tex]y=mx+b[/tex]Isolate y from the given equation to write it in slope-intercept form:
[tex]\begin{gathered} y-250x=500 \\ \Rightarrow y=250x+500 \end{gathered}[/tex]The given equation corresponds to a line with slope 250 and y-intercept 500.
From the image, we can see that the y-intercept is indeed 500, since it is the value of y when x=0.
Notice also that for each increase of 1 unit of the variable x, the variable y increases 250 units. Then, the slope of the graph is 250, the same as the slope of the equation.
We can also check if the equation represents the same line as the graph by evaluating th