A company produces two products, A and B. At least 30 units of product A and at least 10 units of product B must be produced. The maximum number of units that can be produced per day is 80. Product A yields a profit of $15 and product B yields a profit of $8. Let a = the number of units of product A and b = the number of units of product B. What objective function can be used to maximize the profit?
Answers
Let b = units of B produced
At least 30 units of product A and 10 units of product B are required daily, and the maximum number of units per day should not exceed 80.
Therefore
a ≥ 30
b ≥ 10
a + b ≤ 80
Product A yields a profit of $15 and product B yields a profit of $8.
Therefore the objectve profit function is
P(a,b) = 15a + 8b
Answer:
The objective function is
P(a,b) = 15a + 8b, subject to
a >= 30; b>= 10; a+b <= 80
Create a graph that displays the constraints and calculates maximum profit at the boundary points. The solution region is shaded.
The maximum profit occurs when a=70 and b=10.
is the answer
Related Questions
Eddie purchased 4 packages of light bulbs and received a 15% discount. He also paid $4.85 in taxes on his purchase. Write an algebraic expression to represent the total amount Eddie paid. Let x represent the cost of each package purchased.
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There was some gas in the tank. I added 13.3 gallons to it. After that, there was 21 gallons. How many gallons were in the tank at the start?
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17.7
work:
-subtract to find the original number.
21 - 13.3
17.7
hope this helps! :D
Find the slope of each of the lines below:
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The slope is "Undefined".
In how many ways can 15 identical math books be distributed among 6 students?
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A cube has a side of 5 cm. it has a mass of 250 grams. the density of the cube is
Answers
volume cube = side^3 = 5^3 = 125 cm^3, don't forget units!
Density = 250 grams / 125 cm^3 = 2 g/cm^3, with all the units
The density of the cube is calculated to be 2 g/cm³ by dividing the mass (250 grams) by the volume of the cube (125 cm³).
Explanation:To calculate the density of a substance, you divide its mass by its volume. In the given problem, the cube has a mass of 250 grams and each side of the cube is 5 cm. The volume of a cube is calculated by taking the cube of the side length, which in this case is 5^3 = 125 cm³.
By substituting the given mass and computed volume in the formula, we find that the density of the cube is 250 grams ÷ 125 cm³ = 2 g/cm³.
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Find the rectangular coordinates of the point that has polar coordinates , 4, −3π/4
Answers
x= r cosθ
y= r sinθ
r = 4 and θ = −3π/4
cos( −3π/4 ) = cos( 3π/4 ) = cos ( π - π/4) = - cos (π/4)= - √2/2
sin( −3π/4 ) = - sin( 3π/4 ) = - sin ( π - π/4) = -sin (π/4)= - √2/2
x = - 2 √2
y = - 2 √2
Going to be getting a tutor soon but until then I need all the help I can get.
Any help appreciated!
Answers
DFB is obtuse
CFD is a right angle
Rotation
Translation
Reflection
What is [tex] \frac{8m}{n} ^7[/tex] simplified?
Answers
If there are 30 red and 45 blue marbles in a jar with 200 marbles. what percent of the marbles are red
Answers
Number like 10 100,1,000 and so on are called what
Answers
These numbers are called power of ten. A power of ten is 10 multiplied by itself the exponent number of times. For example:
We can write 10 as 10¹
100 as 10²
1000 as 10³
The exponent is equal to the number of zeros in the number like 100 has 2 zeros so the exponent is 2 and write it as 10²
Find out the probability of rolling two dices being total of “7”.
What is all the combination of two dices making total of “7” ?
What is the probability of rolling two dices being total of “7”?
Answers
In how many ways we can get 7:
1) 1+6
2) 2+5
3) 3+4
4) 4+3
5) 5+2
6) 6+1
So there are 6 ways to get a 7,
Hence P(of getting a sum =7) = 6/36 = 1/6 = 0.1667
When two dice are rolled, there are 6 feasible outcomes out of 36 that will sum to '7', hence the probability is 1 out of 6, or approximately 0.167.
Explanation:In the field of probability, when you roll two dice, there are 6 possible outcomes for each die, hence giving us 36 possible outcomes altogether (6*6=36). Out of these 36 possible outcomes, there are 6 combinations that can total to '7'. These combinations are: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). Therefore, the probability of rolling a '7' with two dice is 6 out of 36, which simplifies to 1 out of 6, or approximately 0.167, when rounded to three decimal places.
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If the absolute value of a nonzero real number is equal to the opposite of the number, the number is __________.
positive
negative
zero
irrational
Answers
If the absolute value of a nonzero real number is equal to the opposite of the number then the number is negative.
What is Number system?A number system is defined as a system of writing to express numbers.
We have to find the number for the absolute value of a nonzero real number is equal to the opposite of the number
The absolute value of a number is its numerical value without regard to its sign.
So if the absolute value of a number is equal to the opposite of the number, it means that the sign of the number must be negative.
Hence, if the absolute value of a nonzero real number is equal to the opposite of the number then the number is negative.
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If 2a/b=1/2,what is the value of b/a?
Answers
Answer:
The value of [tex]\frac{b}{a}=4[/tex] .
Step-by-step explanation:
As given in the question
[tex]\frac{2a}{b}=\frac{1}{2}[/tex]
Now find out the value of [tex]\frac{b}{a}.[/tex]
[tex]\frac{b}{a}=\frac{2\times 2}{1}[/tex]
[tex]\frac{b}{a}=2\times 2[/tex]
[tex]\frac{b}{a}=4[/tex]
Therefore the value of [tex]\frac{b}{a}=4[/tex] .
The value of b/a from the equation; 2a/b=1/2 is; 4
Evaluation of inverseThe given equation is;
2a/b=1/2Divide both sides of the equation by 2; we have;
a/b = 1/2 ÷ 2a/b = 1/4Hence, the inverse of a/b is b/a and;
b/a = 4Read more on inverse;
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The Porter family is moving from Baltimore, Maryland, to San Francisco, California. They would like to know what the difference will be in their family budget. How would you explain cost of living to them?
Answers
Answer:
Cost of living is the amount of money needed for fixed expenses such as housing, food, taxes, and health care, as well as variable expenses. Big cities tend to have a higher cost of living than smaller cities.
Step-by-step explanation:
find the value of x for the triangle or rectangle... plz help asap 4 both
Answers
23=x+x+3+2x
23=4x+3
23-3=4x
20=4x
20/4=x
x=5
10.) Perimeter=24
24=x+3+2x+x+3+2x
24=6+6x
24-6=6x
18=6x
18/6=x
x=3
The value of 'x' in a triangle is determined by using the Pythagoras theorem, while in a rectangle, it's determined by algebraic equations.
Explanation:In order to find the value of 'x' in both cases, we need to understand that two different concepts potentially apply; Pythagoras theorem for the triangle, and algebra for the rectangle. The Pythagorean theorem applies to right angle triangles and is expressed as x² + y² = h² where 'x' and 'y' are sides and 'h' is the hypotenuse. In a rectangle, to find 'x' related to an equation like y = 9 + 3x, you substitute values for 'y' and solve for 'x'. An example is given in Table A1 where we see an instance of substituting values for 'x' and then calculating what value of 'y' results. These points are then plotted on a graph.
Learn more about Pythagoras theorem and AlgebraIn exercises 83–86, verify that the intermediate value theorem applies to the indicated interval and find the value of guaranteed by the theorem.
Answers
83.
Given
[tex]f(x)=x^2+x-1[/tex]
on the interval [0, 5], with f(c) = 11
[tex]f(0)=0^2+0-1=-1[/tex]
and
[tex]f(5)=5^2+5-1=25+4=29[/tex]
Clearly, f(c) = 11 is between f(0) = -1 and f(5) = 29
Thus, the intermediate value theorem is satisfied.
To find the value of c, we solve the equation
[tex]c^2+c-1=11[/tex]
as follows:
[tex]c^2+c-1=11 \\ \\ c^2+c-12=0 \\ \\ (c-3)(c+4)=0 \\ \\ c=3 \ or \ -4[/tex]
Because, c is in the interval [0, 5], therefore, the value of c is 3.
84.
Given
[tex]f(x)=x^2-6x+8[/tex]
on the interval [0, 3], with f(c) = 0
[tex]f(0)=0^2-6(0)+8=8[/tex]
and
[tex]f(3)=3^2-6(3)+8=9-18+8=-1[/tex]
Clearly, f(c) = 0 is between f(0) = 8 and f(3) = -1
Thus, the intermediate value theorem is satisfied.
To find the value of c, we solve the equation
[tex]c^2-6c+8=0[/tex]
as follows:
[tex]c^2-6c+8=0 \\ \\ (c-4)(c-2)=0 \\ \\ c=4 \ or \ 2[/tex]
Because, c is in the interval [0, 3], therefore, the value of c is 2.
85.
Given
[tex]f(x)=x^3-x^2+x-2[/tex]
on the interval [0, 3], with f(c) = 4
[tex]f(0)=0^3-0^2+0-2=-2[/tex]
and
[tex]f(3)=3^3-3^2+3-2=27-9+1=19[/tex]
Clearly, f(c) = 4 is between f(0) = -2 and f(3) = 19
Thus, the intermediate value theorem is satisfied.
To find the value of c, we solve the equation
[tex]c^3-c^2+c-2=4[/tex]
as follows:
[tex]c^3-c^2+c-6=0 \\ \\ (c^2+c+3)(c-2)=0 \\ \\ c=2[/tex]
Therefore, the value of c is 2.
86.
Given
[tex]f(x)= \frac{x^2+x}{x-1} [/tex]
on the interval [tex]\left[ \frac{5}{2}, \ 4\right] [/tex], with f(c) = 6
[tex]f\left(\frac{5}{2}\right)= \frac{\left(\frac{5}{2}\right)^2+\left(\frac{5}{2}\right)}{\left(\frac{5}{2}\right)-1}= \frac{ \frac{25}{4}+ \frac{5}{2} }{ \frac{3}{2} } = \frac{35}{4} \cdot \frac{2}{3} =5 \frac{5}{6} [/tex]
and
[tex]f(4)= \frac{4^2+4}{4-1}= \frac{ 16+ 4 }{ 3 } = \frac{20}{3}=6 \frac{2}{3}[/tex]
Clearly, f(c) = 6 is between [tex]f\left(\frac{5}{2}\right)= 5 \frac{5}{6} [/tex] and [tex]f(4)=6 \frac{2}{3}[/tex]
Thus, the intermediate value theorem is satisfied.
To find the value of c, we solve the equation
[tex]\frac{c^2+c}{c-1}=6[/tex]
as follows:
[tex]c^2+c=6(c-1)=6c-6 \\ \\ \Rightarrow c^2-5c+6=0 \\ \\ \Rightarrow(c-2)(c-3)=0 \\ \\ \Rightarrow c=2 \ or \ 3[/tex]
Because, c is in the interval [tex]\left[ \frac{5}{2}, \ 4\right] [/tex], therefore, the value of c is 3.
1. find the LCD of 3/5 and 1/6.
A. 5
B. 6
C. 11
D. 30
2. what is the difference between 3/7 and 1/14.
A. 1\2
B. 4/14
C. 5/14
D. 9/14
3. if Sandy's cookie recipe calls for 1/3 cup of brown sugar and she increases it by 2/9 of a cup, how much brown sugar does she use?
A. 7/9 cup
B. 5/9 cup
C. 4/9 cup
D. 1/9 cup
4. what value could be added to 2/15 to make the sum greater than 1/2?
A. 1/15
B. 8/30
C. 5/15
D. 8/15
5. which set of mixed numbers has a difference less than 1?
A. 1 2/9, 1 1/9
B. 3 4/7, 2 1/7
C. 2 4/5, 1 1/3
D. 2 7/9, 1 1/3
Answers
2. 3/7 - 1/14 = 6/14 - 1/14 = 5/14
3. 1/3 + 2/9 = 3/9 + 2/9 = 5/9
4. 8/15
5. 1 2/9 - 1 1/9
Answer:
1. D. 30
2. C. [tex]\frac{5}{14}[/tex]
3. [tex]\frac{5}{9}[/tex]
4. D. [tex]\frac{8}{15}[/tex]
5. A. [tex]\frac{12}{9}, \frac{11}{9}[/tex]
Step-by-step explanation:
1. LCD or lowest common denominator for a set of fractions is lowest common multiple of all the denominators in that set of fractions
∴ for [tex]\frac{3}{5}[/tex] and [tex]\frac{1}{6}[/tex] LCD will be 5×6 = 30
2. [tex]\frac{3}{7} - \frac{1}{14} = \frac{6-1}{14} = \frac{5}{14}[/tex]
3. [tex]\frac{1}{3} - \frac{2}{9} = \frac{3+2}{9} = \frac{5}{9}[/tex] = [tex]\frac{5}{9}[/tex]
4. [tex]\frac{2}{15} + \frac{1}{15} = \frac{1}{5}\\\\\frac{2}{15} + \frac{8}{30} = \frac{2}{5}\\\\\frac{2}{15} + \frac{5}{15} = \frac{7}{15}\\\\\frac{2}{15} + \frac{8}{15} = \frac{2}{3}[/tex]
5. [tex]\frac{12}{9} - \frac{11}{9} = \frac{1}{9} \\\\\frac{34}{7} - \frac{21}{7} = \frac{13}{7} \\\\\frac{24}{5} - \frac{11}{3} = \frac{17}{15}\\\\\frac{27}{9} - \frac{11}{3} = \frac{-6}{9}[/tex]
What can child-care homes and facilities do to help families and reduce the risk of child abuse?
Answers
They can review staff behavior expectations, have special considerations for very young children and make sure child case spaces are designed well.
Hope This Helps You!
Good Luck :)
Answer:
If a staff member notices behavioral changes in the child it could improve the situation if a staff member subtly questioned the child not alarming anything and if the child is aware of abuse the staff member could quickly respond and seek help from a higher person.
Define a function pyramid volume with double parameters baselength, basewidth, and pyramid height, that returns as a double the volume of a pyramid with a rectangular base. relevant geometry equations: volume = base area x height x 1/3 base area = base length x base width. (watch out for integer division).
Answers
Let f(x) = x2 and g(x) = x − 3. Evaluate (g ∘ f)(0).
Answers
g(f(0)) = 0 - 3 = -3
answer
(g ∘ f)(0) = -3
The value of ( g o f ) (0) is -3.
Here,
The function is given as;
[tex]f (x) = x^{2}[/tex] and [tex]g (x) = x-3[/tex]
We have to find the value of ( g o f ) (0).
What is Composite function?
Composite function is an operation that takes two functions f and g and produces a function k such that k (x) = g(f(x)).
Now,
The function are;
[tex]f (x) = x^{2}[/tex] and [tex]g (x) = x-3[/tex]
Simplify ( g o f ) (0) as;
⇒ [tex]( g o f ) (0) = g ( f (0)) = g (0) = 0-3 = -3[/tex]
Hence, The value of ( g o f ) (0) is -3.
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Jonah is arranging books on a shelf. The order of the books matters to him. There are 336 ways he can arrange the books. Choose True or False for each statement.
Answers
The sum of the probabilities of any event and its complement is always 1.
The student's question involves probability and arrangement of objects, which falls under the subject of mathematics. More specifically, the problem relates to permutations and the fundamental counting principle, combined with basic probability concepts.
Statement 36: The sample space is the set of all possible outcomes that can occur. Since there are 12 different books, the sample space consists of these 12 unique titles, where 8 are fiction (F1 to F8) and 4 are nonfiction (N1 to N4). The sample space is therefore: {F1, F2, F3, F4, F5, F6, F7, F8, N1, N2, N3, N4}.
Statement 37: The sum of the probabilities of an event and its complement is always 1. This is because an event and its complement together cover all possible outcomes in the sample space.
Hellllp pleaseeeee !
Answers
(11p + 3q + 4) + (-5p + 8q)
Answers
6p + 11q + 4 is your answer
hope this helps
How to complete the square when a is greater than 1?
Answers
example :
2x^2 + 6x + 3 = 0.....x^2 has to have a coefficient of 1 in order to complete the square. So, in this case, we divide everything by 2.
x^2 + 3x + 3/2 = 0....now u move the constant over
x^2 + 3x = -3/2...and continue as usual.
just remember, u have to divide by the coefficient of x^2 before moving the constant over.
To get the perfect square when a is greater than 1 divide the whole equation by a.
When a given expression is simplified to the square of a sub-function is called a perfect square.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let's presume with an example,
ax² + bx + c =0
In order to get the perfect square the whole equation must be divided by a for a greater than 1
x² + b/a x + c/a = 0
Thus, to get the perfect square when a is greater than 1 divide the whole equation by a.
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Convert 5.4 ⋅ 103 to standard form.
Answers
_____________________________
Lucy is thinking of a number. the number is greater than two hundred twenty-five. her number is less than 2hundred, 2 tens,7 ones. what is lucy number? howq do i solve this
Answers
so the answer is 226 coz its smaller than 227 and larger than 225
The mean lifespan of a sylvania light bulb is 1600 hours with a standard deviation of 300 hours, an iqr of 450 hours, and a range of 690 hours. the lifespan distribution is relatively symmetric. which measure of spread is the best measurement?
Answers
Since, the distribution is relatively symmetric, the measure of spread that is the best measurement is the standard deviation.
Identify a reflection about the x-axis or a reflection about the y-axis of ƒ(x) = 7x2 – x3 by observing the equation of the function g(x) = –7x2 + x3.
Answers
The function g(x) = –7x² + x³ is the reflection of the function f(x) = 7x² – x³ about the x-axis. This is observed by the change in signs of each term in the function's equation after performing the reflection.
Explanation:By observing the given equation, f(x) = 7x² – x³ and g(x) = –7x² + x³, it is clear that the function f(x) reflects about the x-axis to create function g(x). This is indicated by the change of signs of each term in the equation of the function.
To elaborate, a reflection about the x-axis sees a function's equation change y(x) to -y(x). In our example, f(x) becomes -f(x) or –(7x² – x³), which after simplifying gives us –7x² + x³ = g(x). Therefore, g(x) is the reflection of f(x) about the x-axis.
Furthermore, to identify a reflection about the y-axis, observe if the equation changes from f(x) to f(-x). An even function or a function symmetric about the y-axis would not change with this transformation. Conversely, an odd function would change signs, just like our function did when reflecting over the x-axis.
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Tony made 14L of lemonade for a party. His guests drank 9500 mL of the lemonade. How many milliliters of lemonade did tony have left?
Answers
1L = 1000ml
14L = 14000ml
14000-9500 = 4500ml left
How do you find the coordinates of the midpoint of segment VW with the end points of V(-2,-6) and W(x+2, y+3)
Answers
The coordinates of the midpoint of segment VW are (x/2, (y-3)/2).
Explanation:To find the coordinates of the midpoint of segment VW, we can use the midpoint formula.
The midpoint formula states that the x-coordinate of the midpoint is the average of the x-coordinates of the endpoints, and the y-coordinate of the midpoint is the average of the y-coordinates of the endpoints.
Given the endpoints V(-2, -6) and W(x+2, y+3), we can find the x-coordinate of the midpoint by taking the average of the x-coordinates: (-2 + (x+2))/2.
Similarly, we can find the y-coordinate of the midpoint: (-6 + (y+3))/2.
So the coordinates of the midpoint are (x/2, (y-3)/2).