Hi-Tech, Inc., is a computer training company serving metropolitan Toronto, Canada. The firm contracts a group of part-time instructors to teach a variety of courses concurrently at its downtown location. While demand is so high that any class offered will be filled immediately, Hi-Tech is looking at only two courses at this time: Introduction to Computers (ITC) and Creation of Web Pages (CWP). Each ITC class requires 7.5 hours of preparation/instruction time and contributes a profit of $720, whereas each CWP class calls for only 3 hours and contributes $300. Available time for these two courses is limited to 56 hours a day. There is a restriction on the maximum number of trainees that can be efficiently handled. More specifically, at most 100 students can be accommodated on a daily basis without putting a strain on the facility and support staff. Additionally, each course has a class size limit - 6 for ITC and 12 for CWP. Hi-Tech would like to maximize the daily total profit from both courses so that it could offer certain other courses on a "goodwill" basis. Formulate an AILP for management to decide how many classes should be scheduled for each subject daily
What is the objective function?
Answers
Answer:
The AILP for management to decide how many classes should be scheduled for each subject daily is
The objective function is mathematically represented as
\(M = P_c * a + P_w * b\)
=> \(M = 720 a + 300 b\)
Now the first constraints to this functions is
\(t_c * x + t_w * y \le t_a\)
=> \( 7.5 x + 3 y \le 56\)
Another constraints to this function is
\(k x + u y \le N\)
=> \(6 x + 2 y \le 100\)
Here x and y are the number of classes
Step-by-step explanation:
From the question we are told that
The time required for each ITC class is \(t_c = 7.5 \ hours\)
The profit of each ITC class is \(P_c = \$ 720\)
The time require for CWP class is \(t_w = 3 \ hours\)
The profit for CWP class is \(P_w = \$ 300\)
The total time available is \(t_a = 56 \ hours / day\)
the maximum number of trainee that can be accommodated in a daily basis is \(N = 100\)
The class size limit for ITC is \(k =6\)
The class size limit for CWP is \(u =12\)
Generally the aim of Hi-Tech is to maximize profit
So the objective function will be a function that maximizes profit
Generally the objective function is mathematically represented as
\(M = P_c * a + P_w * b\)
=> \(M = 720 a + 300 b\)
Now the constraints to this functions are
\(t_c * x + t_w * y \le t_a\)
=> \( 7.5 x + 3 y \le 56\)
Another constraints to this function is
\(k x + u y \le N\)
=> \(6 x + 2 y \le 100\)
Here x and y are the number of classes
Related Questions
OK for real this is a hard only verified experts can do this!!!!
Answers
The numeric value of the exponential expression in this problem is given by the following option:
A. 2^12.
How to obtain the numeric value of the exponential expression?The exponential expression for this problem is defined as follows:
8^x/2^y.
8 is the third power of 2, hence:
8 = 2^3.
When a term is elevated to two of it's powers, the powers are multiplied, hence:
(2^3)^x = 2^(3x).
Meaning that the exponential expression is then written as follows:
8^x/2^y = 2^(3x)/2^y.
When two terms of the same base and different exponents are divided, we keep the base and subtract the exponents, hence the expression is given as follows:
2^(3x)/2^y = 2^(3x - y).
As stated in the problem, the numeric value of the expression 3x - y is given as follows:
3x - y = 12.
Hence the entire expression is simplified as follows:
2^(3x - y) = 2^12.
Meaning that the correct option is given by option A.
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Answer:A. 2^12.
Step-by-step explanation:i did it and got it right
What is the total surface area
Answers
Answer:
Step-by-step explanation:
In Exercises 15-18, find the coordinates of the centroid of the triangle with the given vertices. (See Example 2.) 15. A(2,3), B(8,1), C(5,7)
Answers
9514 1404 393
Answer:
(5, 3 2/3)
Step-by-step explanation:
The centroid coordinates are the average of the vertex coordinates.
(A+B+C)/3 = ((2, 3) +(8, 1) +(5, 7))/3 = (2+8+5, 3+1+7)/3 = (15, 11)/3
The centroid is (5, 3 2/3).
_____
The graph shows the intersection of the medians. It is the centroid, (5, 3 2/3), as we calculated.
Is j = 1 a solution to the inequality below? 4 > j
Answers
Answer:
yes
Step-by-step explanation:
4 > j ( substitute j = 1 )
4 > 1 ← is a true statement
so j = 1 is a solution to the inequality
Show that the equation x^4/2021 − 2021x^2 − x − 3 = 0 has at least two real roots.
Answers
The roots of an equation are simply the x-intercepts of the equation.
See below for the proof that \(\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}\) has at least two real roots
The equation is given as: \(\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}\)
There are several ways to show that an equation has real roots, one of these ways is by using graphs.
See attachment for the graph of \(\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}\)
Next, we count the x-intercepts of the graph (i.e. the points where the equation crosses the x-axis)
From the attached graph, we can see that \(\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}\) crosses the x-axis at approximately -2000 and 2000 between the domain -2500 and 2500
This means that \(\mathbf{\frac{x^4}{2021} = 2021x^2 - x - 3 = 0}\) has at least two real roots
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The students in Class 6 vote to pick a class captain. The choice is Anton, Eva, Kofi or Petra. Anton gets 0.2 of the votes. Eva gets 10% of the votes. Petra gets of the votes. Kofi gets 9 votes. How many students are in class 6?
Answers
Answer:
There are 15 students in class 6
Step-by-step explanation:
Let's call the number of students in class 6 "n".
We know that:
Anton gets 0.2 * n votes
Eva gets 0.1 * n votes
Petra gets (1 - 0.2 - 0.1) * n votes
Kofi gets 9 votes
The total number of votes is n, so we can write:
n = 0.2 * n + 0.1 * n + (1 - 0.2 - 0.1) * n + 9
Simplifying this equation:
0.6 * n = 9
So:
n = 9 / 0.6
n = 15
(-2) +[(-13) +4]=[(-2) +(13) ]+4
Answers
Solve proportion round it to the nearest hundredth
Answers
Answer:
7.7 = 2.3
3.6 b
7.7b= 8.28
7.7 7.7
b = 1.075324675
b = 1.08
A) If the last digit in the fractional part of 1.080 is less than 5, then simply remove the last the digit of the fractional part. With 1.080, rule A applies and 1.08 rounded to the nearest hundredth is:
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
Answers
Answer:
x=25
Step-by-step explanation:
2x-14=36
2x=50
x=25
Mrs. Danforth packed $5$ bags of fun-sized candies for her family's picnic. Each bag contains $16$ pieces. She had intended to pass out the same number of candies to each of her $4$ children. But Cameron, her second-youngest, argues that she should instead distribute the candies in proportion to the children's ages. All of the children have different ages. If Cameron can convince his mother to give out the candies his way, he will gain two candies while his four-year-old sister will lose twelve. How old is Mrs. Danforth's oldest child?
Answers
From the information given in the word problem, the oldest child of Mrs. Danforth must be 13 years old.
What is the calculation showing the above?
Given:
Each bag contains $16 CandiesThere are 5 bagsThere are four children.Since the bags are distributed according to the proportion of their ages, then, we say
5 bags x 16 candies =80 candies.
80 / 4 = 20 candies per child
Given that his 4-year-old sister gets 20 -12 = 8 candies, then:
8/4 = 2 candies per year for each child's age.
Given that Cameron will gain 20 + 2 =22 candies, then:
22 / 2 = 11 years is Cameron's age.
22 candies of Cameron + 8 candies for youngest sister=30
80 - 30 = 50 candies for the remaining older children.
Since Cameron is the 2nd youngest, it means the remaining 2 siblings must be 12 and 13 years respectively:
So that: 12 x 2 = 24 candies for the 3rd oldest
And 13 x 2 = 26 candies for the oldest child. So, the total allocations of all the candies would be:
8 + 22 + 24 + 26 = 80 candies.
Therefore, the most senior child must be 13 years old.
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Full Question
Mrs. Danforth packed 5 bags of fun-sized candies for her family's picnic. Each bag contains 16 pieces. She had intended to pass out the same number of candies to each of her 4 children. But Cameron, her second-youngest, argues that she should instead distribute the candies in proportion to the children's ages. All of the children have different ages. If Cameron can convince his mother to give out the candies his way, he will gain two candies while his four-year-old sister will lose twelve. How old is Mrs. Danforth's oldest child?
a store is selling laptops with six different operating systems. a company would like to buy 35 of those laptops for their employees. in how many ways can this company buy them?. show all your work step by step to get credit. final answers must be provided in decimal form
Answers
On solving the provided question, based on the information, we can say that there are 35 X 6 = 210 ways
What are combinations?Combining means selecting all or part of a set of objects, regardless of the order in which the objects are selected. Suppose we have a set of three characters.
\(^nC_{r} = \frac{n!}{r!(n - r)!}\)
ways can this company buy them are - 35 X 6 = 210 ways
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How do you solve 3p+12<12
Answers
Answer:
The answer is p<0.
Step-by-step explanation:
You solves by, wait, I'll just show you. :D
3p+12<12
-12 -12
------------------
3p<0
Then, divide 3 from both side.
Therefore, p<0.
Btw if you divide by a negative you switch the sign the other way, like >.
Answer:
The answer is 0.
Step-by-step explanation:
You subtract 12 from both sides
ex: 3p+12-12<12-12
You'll have 3p<0
LASTLY you divide both sides from 3
\(\frac{3p}{3} < \frac{0}{3}\)
Question 3 (1 point)
(08.02 LC)
Complete the square to transform the expression x² + 4x + 2 into the form a(x - h)² + k.
O a
Ob
Oc
Od
(x + 2)²-2
(x + 2)² +2
(x+4)²-2
(x+4)²+2
Answers
Answer:
The answer to your problem is, A. (x + 2)²-2
Step-by-step explanation:
\(x^{2}\) + 4x + 2
= \(x^{2}\) +4x + 4 -2
= (x + 2)²-2 ← Answer
Thus the answer to your problem is, A. (x + 2)²-2
11-5×(-14+2) need help solving this
Answers
Answer: We have to simplify the expression, it can be done as follows.
\(11-5\cdot(-14+2)=11-5\cdot(-12)=11-(-60)=71\)Therefore this is the answer.!
6. Given AACP ALNX, find each missing measure. N 29° 13 cm P CX V L 21 cm a) XL = b) AC= c) PC = d) m/L= e) m/C= f) m/X=
Answers
The missing measure is ∠P =∠X = 122°
Given △ACP ≅ △LNX
XL = 13 cm, m∠L = 29°
AC = 21 cm, m∠C = 29°
PC = 13 cm, m∠Y = ?? (there is no angle Y)
On the right shows the triangles are isosceles, with XL = XN. That means also PA = PC. Those side lengths are all the same: 13 cm.
PA = PC = XL = XN = 13 cm
In the same way, ...
LN = AC = 21 cm
Of course, the angles have a similar relationship:
∠A = ∠C = ∠L = ∠N = 29°
The two base angles in the triangle add to 58°, so the third angle is ...
180° -58° = 122°
∠P =∠X = 122°
As is often the case in over-specified problems, the numbers shown are not consistent. The length LN is actually incorrect for the angle and side specified for triangle ACP, or the angles are incorrect for the side lengths specified. What this means is that the answers you get will depend on how you work the problem. Above, we have taken the given numbers and relationships at face value, even though we know they are incorrect.
Hence the answer is The missing measure is ∠P =∠X = 122°
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3 problems for 1 final answer. fairly easy 8th grade math.
Answers
When we evaluate the given expression, A/5 + √(B - C), the result obtained is 9 (option B)
How do i determine the value of A/5 + √(B - C)?
First, we shall determine the value of A. Details below:
A = Product of roots in x² - 11x + 30Value of A =?Quadratic equation is expressed as:
x² - (sum of root)x + product of root
Comparing the above with x² - 11x + 30, we have
x² - 11x + 30 = x² - (sumof root)x + product of root
Product of roots = 30
Thus,
A = 30
Next, we shall determine the value of B. details below:
f(x) = x² + 5Value of B = f(2) =?f(x) = x² + 5
f(2) = 2² + 5
f(2) = 9
Thus,
B = 9
Next, we shall determine the value of C. Details below:
(x² - 2x - 24) / (x + 4)Value of C = Remainder =?Let
x + 4 = 0
Thus,
x = -4
Substitute the value of x into x² - 2x - 24 to obtain the remainder as shown below:
Remainder = x² - 2x - 24
Remainder = (-4)² - 2(-4) - 24
Remainder = 0
Thus,
C = 0
Finally, we shall determine value of A/5 + √(B - C). Details below:
A = 30B = 9C = 0Value of A/5 + √(B - C) =?A/5 + √(B - C) = 30/5 + √(9 - 0)
A/5 + √(B - C) = 6 + √(9
A/5 + √(B - C) = 6 + 3
A/5 + √(B - C) = 9
Thus, the value of A/5 + √(B - C) is 9 (option B)
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What factoring method would be the BEST choice
4x² - 121
Answers
( 2x + 11 ) ( 2x - 11 ) is factor of linear equation .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
A linear equation with one variable is one that contains just one variable. It has the mathematical formula Ax + B = 0, where A and B can be any two real numbers, and x is an unknowable variable with just one possible value.
= 4x² - 121
= (2x)² - ( 11 )²
= ( 2x + 11 ) ( 2x - 11 )
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Determine whether the set of points represent a function relationship.
(2, 4) (4, 6) (6, 8) (3,4) (5,7) (8,2) is this a function?
Answers
Answer:
\(\textsf {Yes}\)
Step-by-step explanation:
\(\textsf {A function contains a set of pairs where each x only has a single y.}\)
\(\textsf {Here, all x values are different, so we can confirm that this is indeed a functon.}\)
Please help me determine if these sequence are arithmetic geometric or neither
Answers
Given:
\(\begin{gathered} a(1)=5,a(n)=a(n-1)+3\text{ }for\text{ }n\ge2 \\ b(1)=1,b(n)=3.b(n-1)for\text{ }n\ge2 \\ c(1)=3,c(n)=-c(n-1)+1\text{ }for\text{ }n\ge2 \\ d(1)=5,d(n)=d(n-1)+n\text{ for n}\ge2 \end{gathered}\)Required:
Find whether the series is arithmetic or geometric.
Explanation:
(1) The given terms are
\(5,8,11,14,17\)Find the common difference of the following terms.
\(\begin{gathered} 8-5=3 \\ 11-8=3 \\ 14-11=3 \\ 17-14=3 \end{gathered}\)The common difference is the same between each term so the given sequence is arithmetic.
(2)The given terms are
\(1,3,6,9,12,15\)Find the common difference as:
\(\begin{gathered} 3-1=2 \\ 6-3=3 \\ 9-6=3 \end{gathered}\)Since the common difference is not the same between each term so the given sequence is not arithmetic.
Now find the common ratio as:
\(\begin{gathered} \frac{3}{1}=3 \\ \frac{6}{3}=2 \\ \frac{9}{6}=\frac{3}{2} \end{gathered}\)Since the common ratio is not the same between each term so the given sequence is not geometric.
Thus the given sequence is neither arithmetic nor geometric.
(3)The given terms are
\(3,-2,-5,-8,-11\)Find the common difference as:
\(\begin{gathered} -2-3=-5 \\ -5-(-2)=-5+2=-3 \\ -8-(-5)=-8+5=-3 \end{gathered}\)Since the common difference is not the same between each term so the given sequence is not arithmetic.
Now find the common ratio as:
\(\begin{gathered} \frac{-2}{3}=-\frac{2}{3} \\ \frac{-5}{-2}=2.5 \end{gathered}\)Since the common ratio is not the same between each term so the given sequence is not geometric.
Thus the given sequence is neither arithmetic nor geometric.
(4) The given sequence is:
\(d(1)=5,d(n)=d(n-1)+n\text{ for n}\geqslant2\)\(\begin{gathered} d(2)=d(2-1)+2 \\ =d(1)+2 \\ =5+2 \\ =7 \end{gathered}\)\(\begin{gathered} d(3)=d(3-1)+3 \\ =d(2)+3 \\ =7+3 \\ =10 \end{gathered}\)\(\begin{gathered} d(4)=d(4-1)+4 \\ =d(3)+4 \\ =10+4 \\ =14 \end{gathered}\)\(\begin{gathered} d(5)=d(5-1)+5 \\ =d(4)+5 \\ =14+5 \\ =19 \end{gathered}\)Thus the terms of the sequence are 5,7,10,14,19.
Simplify:
|-12-3|/4| - | 23-42/8 |
A: 15/4
B: 21/4
C: 11/8
D 19/8
Answers
The absolute value expression can be rewritten as 11/8, thus, the correct option is C.
How to simplify the expression?Here we want to simplify the expression:
|(-12 - 3)/4| - |(23 - 42)/8|
the denominators can be rewritten as:
-12 - 3 = -15
23 - 42 = -19
Then we can rewrite:
|-15/4| - |-19/8|
Remember that the absolute values have positive outcomes, then we can rewrite this as:
15/4 - 19/8
30/8 - 19/8
11/8
The correct option is C.
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Answer:
c
Step-by-step explanation:
Fill in the table using this function rule.
A
y=-6x+1
X
-5
-1
0
1
1
0
0
X
3
Answers
As per the given function rule , y = -6x + 1 , the values will be 31, 7, 1, -5 -5 , 1, 1, -6X+1, -17.
What are functions?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).
What is a function rule?The relationship between the input or domain and the output or range is known as the function rule. If and only if there is a single value in the range for each domain value, a relation is a function.
As per the given function rule in the question i.e y = -6x + 1
X Y
-5 31
-1 7
0 1
1 -5
1 -5
0 1
0 1
X -6X +1
3 -17
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QUICK PLS.
The sum of the measures of angle P and angle S is 140°.
• The measure in degrees of angle P is represented by the expression (5x + 30)°.
• The measure of angle S is 80°.
What is the value of x?
A. 38
B. 6
C. 10
D. 22
My teacher never reviews things correctly
Answers
Answer:
The anwser i think it's D
Step-by-step explanation:
What is the probability that a 5-card straight flush will be drawn (a straight flush is 5 cards in a row, all cards the same suit) if the first two cards drawn are the 2 of spades and the 6 of spades
Answers
Answer:
\(\mathbf{\dfrac{1}{19600}}\)
Step-by-step explanation:
From the information given:
For 5 cards to be drawn where the first two are 2 spades and 6th of the spade.
Then the cards should be: 2,3,4,5,6 of spade.
Since 2 and 6 are already drawn.
Then;
the 3rd card maybe 3, 4, or 5 of the spade.
Thus, the probability that it is the third card is: 3/50
The probability is the 4th card 2/49 ; &
The probability that it is the fifth card is 1/48
Thus, the probability that a 5-card straight flush is drawn is:
\(P(5) = 1 \times 1\times \dfrac{3}{50}\times \dfrac{2}{49} \times \dfrac{1}{48}\)
\(P(5) = \dfrac{1}{19,600}\)
Please help me in this math problem
Answers
Answer:
Step-by-step explanation: well, you will more than likely get it at least 60%-80% of the time! If this doesn't help i can try to explain in a lot more detail unless someone does for me!
the area of a rectangle is x2-13x+36 cm2. if its width is x-4 cm, what is length
Answers
Answer:
hi
Step-by-step explanation:
lolol
Pls help I need this answer now As part of a class project, a university student surveyed the students in the cafeteria lunch line to look for a relationship between eye color and hair color among students. The table below contains the results of the survey.
Answers
Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63. Option D
To find the relative frequency of students with red hair among the sample population of students with gray eyes, we need to divide the number of students with gray eyes and red hair by the total number of students with gray eyes.
From the given table, we can see that there are 22 students with gray eyes and red hair.
The total number of students with gray eyes is the marginal total for gray eyes, which is 35.
To find the relative frequency, we divide the number of students with gray eyes and red hair by the total number of students with gray eyes:
Relative frequency = Number of students with gray eyes and red hair / Total number of students with gray eyes
Relative frequency = 22 / 35
Simplifying the fraction, we have:
Relative frequency = 0.6286
Rounding the answer to two decimal places, the relative frequency of students with red hair among the sample population of students with gray eyes is approximately 0.63.
Therefore, the correct answer is option OD) 0.63.
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A farmer sold 54 pumpkins the first weekend of a fall festival and 42 pumpkins the second weekend.
Which expression uses the distributive property to show equivalent expressions for this situation?
54 + 42 = (3)(18) + (6)(7)
54 + 42 = (9)(10) + 6
54 + 42 = 90 + 6
54 + 42 = 6(9 + 7)
Answers
Answer:
54 + 42 = 6(9 + 7)
Step-by-step explanation:
Using distributive property on the right side of the equality, you multiply 6 and nine and 6 and 7 to get rid of the parenthesis.
Answer:
its the last one
Step-by-step explanation:
The function f(x) = −(x + 5)(x + 1) is shown. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 3, 4), and goes through (negative 1, 0). What is the range of the function? all real numbers less than or equal to 4 all real numbers less than or equal to −3 all real numbers greater than or equal to 4 all real numbers greater than or equal to −3 Mark this and return
Answers
Answer:
All real numbers less than or equal to 4.
f(x) ≤ 4
Interval notation: (-∞, 4]
Step-by-step explanation:
Given the quadratic function, f(x) = -(x + 5)(x + 1), where the vertex occurs at point, (-3, 4):
Since the graph of the parabola opens down, then it means that the vertex is its maximum point. In reference to the vertical points on the graph (i.e., the range values), then the vertex sets the maximum range value of k = 4. This implies that the maximum possible range value is from negative infinity to positive 4.
Therefore, the range of the function is: all real numbers less than to or equal to 4.
f(x) ≤ 4
Interval notation: (- ∞, 4]
Answer:
its A on edge
Step-by-step explanation:
Just took the test
Rotation - Question 5
Answers
When the former image is rotated, the dots will be located at section 2 and 7.
What is the effects of image rotation?When an image is rotated, the constituents within it also changes its position as the object is moves from a point to another about a pivot junction.
From the given image above, after the rotation of the initial image, the dot should be located at number 2 and 7 of the new image.
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40 POINTS PLEASE HELP ASAP YOU CAN SAVE MY LIFE WILL GIVE BRANLIEST
Which expression is equivalent to 8\sqrt(6)
A.\sqrt(14)
B.\sqrt(48)
C.\sqrt(96)
D.\sqrt(384)
Answers
Answer:
D. \sqrt(384)
Step-by-step explanation:
All you have to do is to expand the root the way I have done. I hope you understand and rate this answer well.
Don't forget 8 is the same as root(8) * root(8) which will give root(64) and the square root of 64 is 8.
