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 1

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

       [tex]M  =  P_c  *  a  + P_w  *  b[/tex]

=>    [tex]M  = 720  a  + 300  b[/tex]

Now the first constraints to this functions is

     [tex]t_c  *  x  + t_w * y  \le t_a[/tex]

=>  [tex] 7.5  x  + 3 y  \le 56[/tex]

Another constraints to this function is

     [tex]k  x  +  u  y  \le  N[/tex]

=>    [tex]6  x  +  2  y  \le  100[/tex]

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  [tex]t_c  = 7.5 \ hours[/tex]

   The profit of each ITC class is  [tex]P_c  =  \$ 720[/tex]

   The time require for  CWP  class is  [tex]t_w  =  3 \  hours[/tex]

    The profit for   CWP  class is  [tex]P_w  =  \$ 300[/tex]

   The total time available  is [tex]t_a  =  56 \  hours / day[/tex]

   the maximum number of trainee that can be accommodated in a daily basis is   [tex]N  =  100[/tex]

   The class size limit for  ITC  is  [tex]k  =6[/tex]

    The class size limit for CWP is  [tex]u  =12[/tex]

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

       [tex]M  =  P_c  *  a  + P_w  *  b[/tex]

=>    [tex]M  = 720  a  + 300  b[/tex]

Now the constraints to this functions are

     [tex]t_c  *  x  + t_w * y  \le t_a[/tex]

=>  [tex] 7.5  x  + 3 y  \le 56[/tex]

Another constraints to this function is

     [tex]k  x  +  u  y  \le  N[/tex]

=>    [tex]6  x  +  2  y  \le  100[/tex]

Here x and  y are the number of classes

     

   


Related Questions


Michelle has a piece of yarn measuring 7 yards. How many 1-inch strips can be cut from the yarn?

Answers

Answer:

252

Step-by-step explanation:

7 yards is equivalent to 252 inches.

Answer:

252 inches

Step-by-step explanation:

There are 3 feet in 1 yard. Multiply 7 yards x the 3 feet in each 1 yard.

You should now have 21 feet.

Multiply 21 feet x the 12 inches in each foot.

You should come up with 252 inches as your final product.

Which is the last operation when evaluating (8-2x)2+4 for x=3?

Answers

Answer:

addition.

Step-by-step explanation:

(8-2x)2+4

(8-2(3))2+4

(8-6)2+4

(2)2+4

4+4 (last operation)

8

15 POINTS!

An abandoned lot is to be converted into a community garden. The garden is to consist
of a 7 yard by 20 yard rectangle for planting that is surrounded by a path of uniform
width. The total area of the lot is 198 square yards. What is the width of the path?

SHOW WORK PLS TY

Answers

The answer is 7x20 and that equals 140 good luck

What is the equation of the line in slope-intercept form? the line perpendicular to y = x + 2 through (-7, -8)​

Answers

Answer:

[tex]y=-x-15[/tex]

Step-by-step explanation:

Point-slope formula: [tex]y-y_1=m(x-x_1)[/tex], where [tex](x_1, \ y_1)[/tex] are the coordinates of a point on the line, and [tex]m[/tex] is the slope of the line.

You are given a point that the line you are trying to find passes through, and a slope. The slope is less obvious than the point, but you can find the slope using the given information.

The line perpendicular to y = x + 2 will have the opposite reciprocal slope of this line. The slope of y = x + 2 is 1, so the opposite reciprocal of 1 is:

[tex]m=-\frac{1}{1} =-1[/tex]

Now that you have both a point and the slope of the line you are trying to find, you can substitute these values into the point-slope formula (Notice: the name of this formula contains both "point" and "slope").

Substitute [tex](-7, \ -8)[/tex] for [tex](x_1,\ y_1)[/tex] and [tex]m=-1[/tex] into the point-slope formula.

[tex]y-(-8)=-1(x-(-7))[/tex]

Simplify this equation.

[tex]y+8=-1(x+7)[/tex]

Distribute -1 inside the parentheses.

[tex]y+8=-x-7[/tex]

Subtract 8 from both sides of the equation.

[tex]y=-x-15[/tex]

This line is in slope-intercept form ([tex]y=mx+b[/tex]), so we are done.

The perimeter, P, of a square whose side length is n.

Answers

Answer: p = 4n

Step-by-step explanation:

To find the perimeter of a shape, you need to add the length of the 4 sides. A square's 4 sides are equal. Therefore, you add n+n+n+n which is the same as 4n.

Answer:

P = n4

Step-by-step explanation:

in order to find the perimeter of an object you must add up all the sides. since we are dealing with a square all the sides are n. so in conclusion, 4 times n would you get you the perimeter, P.

A=4 b= -5 and c=-8
HELLPPPPPP

Answers

-13:)

Hope this helps
I got -3.

since b = -5, that cancels out the negative and makes b=5.

5+-8 is -3.

Help ASAP). Which relation is a function. Where the hand is at thats graph A across is graph B. The graph under graph a is ( graph C). Under graph B is (graph D). Need answer now please and thank you. [ I chose B but not 100% sure]​

Answers

Graph D, since it passes the vertical line test.

Round 47.58051 to the nearest thousandths

Answers

Answer:

47.581

Step-by-step explanation:

can't explain I just know how to do it

Hector is visiting a cousin who lives 360 miles away. He has driven 70 miles. How many more miles does he need to drive to reach his cousin's home? Let d be how many miles left to reach his cousin's home.

Answers

Answer:

260 miles.  

Step-by-step explanation:

350-90=260  

If you see the word difference in an equation, it means to subtract. :) hope that helps

If M is the midpoint of AB and AM = 3x -1 and AB =5 x + 2, find x, AM, MB, and AB.

Answers

AB = 2x + 3

Just subtract the 3x - 1 from 5x + 2 = 2x + 3 is AB

x = 2

AB = 12

MB = 7

AM = 5

Hope this helps.

What are the x and y-intercepts from the table shown?​

Answers

X intercept is -4,0 and Y is 0,8
X- intercept is -4,0
Y- intercept is 0,8

Someone, please help me.

Answers

I believe the answer would be four since the right and left side are symmetrical, same as the top and bottom

In 1902, the yearly attendance at a major league baseball park was 3.4 × 105 people.
One hundred years later, the yearly attendance was 1.7 × 106 fans.
How many times greater was the attendance in 2002 than in 1902? Enter your answer in the box. helpppppp

Answers

Answer: 1902 had 357 people and 2002 had 180.2 people so, the answer would be  

 

176.8

Step-by-step explanation: i hope  this helps

plz tell me if its wrong so i can fix it

Can anybody graph y= —2x + 5.

Answers

Answer:

The y-intercept is 5 so that is where it will start then just keep going down by 2 since the slope is (-2)

hope this helps =3

What is the average speed of a baseball that is thrown 90 feet in 2 seconds?
A. 180 feet/second
B. 45 feet/second
C. 92 feet/second
D. A variable most often found on the y-axis

Answers

B. 45 feet/second

To find out how fast it can go in 1 second, we divide it by 2
90 divided by 2 is 45, so the average speed of a baseball that is thrown 90 feet in 2 seconds is 45 feet/second
For this answer is b

Maggie bought a pound of bananas and 4 boxes of cereal for $10.11. If each box of cereal cost $2.40, what was the price of a pound of bananas?
$0.51
$0.61
$1.51
$2.91

Answers

Answer:

$0.51

Step-by-step explanation:

If each box of cereal is $2.40, $2.40 multiplied by 4 is $9.60. $10.11 is the total, so $10.11 - $9.60 = $0.51.

Answer:

$0.51

Step-by-step explanation:

the person above me was correct

Can someone please help me!!! Also does anyone know if there is a website or calculator that may give me the answers? Please help me! Thank you!

Answers

Answer:

[tex] x = 17 [/tex]

Step-by-step explanation:

[tex] 2x + 7 = 3x - 10 [/tex] (alternate exterior angles are congruent when a transversal cuts across two straight lines)

[tex] 2x - 3x = -7 - 10 [/tex] (collecting like terms)

[tex] - x = -17 [/tex]

[tex] \frac{-x}{-1} = \frac{-17}{-1} [/tex] (dividing both sides by -1)

[tex] x = 17 [/tex]

Can some please tell me what this is?

Answers

Step-by-step explanation:

This is mean domain is all real numbers

X = all real numbers or ALM or that R symbol

2x+ 8y = -3
3x+ 6y = -4
Choose all answers that apply

Answers

multiply the top equation by 3, multiply the bottom equation by 4, then subtract the bottom equation from the top equation

multiply the top equation by 3, multiply the bottom equation by -2, then add the equations

If f(x) = 8x+9 and g(x) = 4x-3, what is (f+g)(x)?
O A 4x-12
B. 4x+12
0
C 12x+6
D. 32x-27

Answers

I think is c that what i think
I think it’s c that’s what I think

Annabel wants to buy a $50.00 jacket that is marked 30% off. What is the final cost of the jacket (after the discount)?

Question 1 options:

$15.00


$35.00


No Solution


$65.00

Answers

Answer:

$ 35.00

Step-by-step explanation:

50.00 ÷ 10 = 5.00 (10%)

5.00 x 3 = 15.00 ( 30%)

50 - 15 = 35.

Sorry I couldn't explain more, But I hope this helps!

A system of equations is shown.
- x + 3y = 9
x = 1 - 2y
What is the solution of the system?
A. (-19, 10)

B. (-6, 7/10)

C. (-9/2, 9/2)

D. (-3,2)

Answers

Answer:

c

......................

Step-by-step explanation:

.....................

Answer:

c

Step-by-step explanation:

Help Please I Really Need Help

Answers

Answer:

X=5

Step-by-step explanation:

3x+4=19

3x+4-4=19-4

3x=15

15/3x=

X=5

Hope this helps!

mike is 46 yrs old. He is 4 yrs older than 3 times his son Jared's age. Find Jared's age

Answers

Answer:

Jared is 14 years old

Step-by-step explanation:

HELP ILL GIVE BRAINLIEST HELPPPP

Answers

EFGH-
Db = 6
Ac = 9

IJKL-
Db = 2
Ac = 3

I hope this helps

PLEASE HELP MEEEEEEE I NEED THIS QUICK
Which of the following best defines the two quantities that are measured to find the call rate of a phone company? (5 points)
Group of answer choices

The quantity of price measured in dollars depends on the quantity of time measured in minutes.

The quantity of time measured in minutes depends on the quantity of price measured in dollars.

The quantity of time measured in minutes depends on the quantity of speed measured in calls per minute.

The quantity of speed measured in calls per minute depends on the quantity of time measured in minutes.

Answers

Answer:

A: The quantity of the price would be measured in dollars depends on the quantity of time measured in minutes.

Step-by-step explanation:

A seemed like the best answer to me. I hope I helped

ve spent the whole weekend grading math assignments. I graded 30 students
work this weekend, which is 40% of my class. How many students do I have in
my class?

Answers

Answer:

75

Step-by-step explanation:

How many students is 1% of the class, 30/40=0.75, so you could do 0.75x100=75, or you could do 0.75x60=45, and 45+30=75.

g The average lifespan for a certain type of vehicle is 8 years and follows an exponential distribution. A lot contains 200 of these vehicles, brand new. What is the probability that 50 or more of them fail in the first 2 years

Answers

Answer:

The probability is [tex]P(A \ge 50 ) = 0.14321[/tex]

Step-by-step explanation:

The average life span is  [tex]\pi = 8[/tex]

The sample size is n =  200

Generally we are told that average lifespan for a certain type of vehicle follows an exponential distribution

i.e  

             [tex]X \~ \ \ \ exp(8)[/tex]

Gnerally the probability distribution function for exponential distribution is

       [tex]f(x) = \left \{ {{\lambda * e^{-\lambda * x }\ \ \ x\ge 0 } \atop {0 \ \ \ \ \ \ \ \ \ \ x < 0}} \right.[/tex]

Now [tex]\lambda[/tex] is the  constant which is evaluated as

      [tex]\lambda = \frac{1}{\pi}[/tex]

=>   [tex]\lambda = \frac{1}{8}[/tex]

=>   [tex]\lambda = 0.125[/tex]

Generally the that the vehicles will fail in less than 2 years is  mathematically represented as

         [tex]P(X \le 2 )= p= \int\limits^2_0 {\lambda e^{- \lambda * x} } \, dx[/tex]

        [tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * x} } ]|\left 2 } \atop {0}} \right.[/tex]

       [tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 2} } ] - [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 0} } ][/tex]

     [tex]P(X \le 2 )= p= -0.77880 + 1[/tex]

     [tex]P(X \le 2 )= p= 0.2212[/tex]

Generally the probability that the vehicle will fail in the first 2 years follows a binomial  distribution  with the mean evaluated as

         [tex]\mu = n * p[/tex]

=>      [tex]\mu = 200 * 0.2212[/tex]

=>      [tex]\mu = 44.24[/tex]

The standard deviation is

       [tex]\sigma = \sqrt{np(1 - p)}[/tex]    

      [tex]\sigma = \sqrt{200 * 0.2212 (1 - 0.2212)}[/tex]  

      [tex]\sigma = 5.86[/tex]

Using normal approximation of binomial  distribution the  probability that 50 or more of them fail in the first 2 years is mathematically represented as

   [tex]P(A \ge 50 ) = 1 - P(A < 50 )[/tex]

Applying continuity correction

    [tex]P(A \ge 50.5 ) = 1 - P(A < 50.5 )[/tex]

Here

    [tex]P(A < 50.5 ) = P(\frac{A - \mu }{\sigma} < \frac{50 - 44.24}{5.87} )[/tex]

Generally  

       [tex]\frac{A - \mu }{\sigma} = Z (The \ standardized \ value \ of A )[/tex]

=> [tex]P(A < 50.5 ) = P( Z < 1.0664 )[/tex]

From the z-table the probability value  of  ( Z  <  1.0664   ) is  

     [tex]P( Z < 1.0664 ) = 0.85679[/tex]

So  

   [tex]P(A \ge 50 ) = 1 - 0.85679[/tex]

=> [tex]P(A \ge 50 ) = 0.14321[/tex]

Simplify -√36 please

Answers

Answer:

-6

Step-by-step explanation:

djhcjici4n c rncinr

for the question the answer will be -6

3x+2=11 what is the answer

Answers

Answer:

x = 3

Step-by-step explanation:

Hi there !

3x + 2 = 11

3x = 11 - 2

3x = 9

x = 9/3

x = 3

Good luck !

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