2. JOY leather, a manufacturer of leather Products, makes three types of belts A, B and C which are processed on three machines M1, M2 and M3. Belt A requires 2 hours on machine (M1) and 3 hours on machine (M2) and 2 hours on machine (M3). Belt B requires 3 hours on machine (M1), 2 hours on machine (M2) and 2 hour on machine (M3) and Belt C requires 5 hours on machine (M2) and 4 hours on machine (M3). There are 8 hours of time per day available on machine M1, 10 hours of time per day available on machine M2 and 15 hours of time per day available on machine M3. The profit gained from belt A is birr 3.00 per unit, from Belt B is birr 5.00 per unit, from belt C is birr 4.00 per unit. What should be the daily production of each type of belt so that the profit is maximum?
a) Formulate the problem as LPM
b) Solve the LPM using simplex algorithm.
c) Interpret the shadow prices

The shadow price of a constraint, the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.

A constraint is a condition of an optimization problem that should be satisfied the condition.

We can formulate this problem as a linear programming model (LPM):

Suppose X1 be the number of belt A produced per day, X2 be the number of belt B produced per day and X3 be the number of belt C produced per day

The objective function is to maximize the profit;

3X1 + 5X2 + 4X3.

The constraints are as :

The time spent on machine M1 must be less than or equal to 8 hours per day so we get;

2X1 + 3X2 <= 8

The time spent on machine M2 must be less than or equal to 10 hours per day so we get;

3X1 + 2X2 + 5X3 <= 10

The time spent on machine M3 must be less than or equal to 15 hours per day so we get

2X1 + 2X2 + 4X3 <= 15

Thus number of belts produced must be positive:

X1, X2, X3 >= 0

To solve this LPM using the simplex algorithm,

Also the objective function is to minimize the cost, and all constraints are in the form of "less than or equal to" a certain value.

The pivot row is the row that corresponds to the smallest positive ratio between (RHS) value and the corresponding pivot column element the constraint 2X1 + 3X2 ≤ 8.

Now Interpret the shadow prices.

The shadow price of a constraint is the change in the objective function value for a unit change in (RHS) value of the constraint, with all other variables held constant.

Here the value of the constraints in the LPM and how they contribute to the optimal solution.

Learn more about constraints;

brainly.com/question/14438192

#SPJ1

PLEASE HELP 0ffering MAX POINTS

help me please i will give you brainliest

if a city with a population of 500,000 doubles in size every 64 years, what will the population be 256 years from now?

The teachers at Eastside High School were asked the number of years they have been teaching. The results are as follows.

3, 4, 9, 12, 7, 5, 4, 12, 3, 9, 11, 4, 14, 9, 2, 10, 3, 10, 9, 7

Use the data to fill in the box-and-whisker plot below.

260 students were surveyed on whether they prefer apple juice or orange juice. A table of relative frequencies is shown. How many more girls prefer apple juice than boys

Find the value of x.

(10x – 2) - (2x - 7)
O 8x + 5
O 12.2 + 5
o 12c - 9
O 83 -9

uld observe for the entire population represented by the volunteers if all members of this population tasted, respectively, the yogurt with and without the added calcium. If we had used the more accurate software approximation for the degrees of freedom, how would the 90% confidence interval compare to the one constructed with the more conservative value for degrees of freedom

According to the Central Limit Theorem, which statements(s) are TRUE. There may be more than 1 correct answer. A. An increase in sample size from n = 16 to n = 25 will produce a sampling distribution for the sample means that has a smaller standard deviation. B. The larger the sample size, the more the sampling distribution of sample means will resemble a normal distribution C. The mean of the sampling distribution of sample means for samples of size n = 15 will be the same as the mean of the sampling distribution for samples of size n = 100. D. The mean of a sampling distribution of sample means is equal to the population mean divided by the square root of the sample size. E. The larger the sample size, the more the sampling distribution of sample means resembles the shape of the population.

Brainliest for correct answer

The volume of this rectangular prism is 240 cubic centimeters. What is the surface area?

-6y+15= -27 what is y?

Find two numbers which add to give 0 and multiply to give -16

Factor and solve 121r^2-64t^2

There are 6 flavors of candy in a bag. The probability of randomly selecting strawberry is 1/4, lime is 3/16, lemon is 4/32, cherry is 1/8, and grape is 14/64. What is the probability of randomly selecting a piece of the 6th flavor?

Can you plz help me by solving the equation and showing how you got the answer

Find which of the following fractions is larger: 51) 2/5,1/3,1/15 A) 2/5 B) 1/3 C) 1/15
52) 3/12,2/6, 1/24 A) 3/12 B) 2/6 C) 1/24​

i don’t need to show work but it would help :)

Determine whether the equation represents direct, joint, or inverse variation. Then identify the constant.
t = 100/s
y/5 = x
p/qr = 4
C = 2πr
V = 1/3πr^2h
xy = 2/5

If log 7 =0.845, find log (7200).

The perimeter of any polygon is the?
Choose a right answer :
a) Product of all the sides.
b) sum of the all sides.
c) sum of any two sides.
d) sum of the diagonals.​

What is the value of the following
expression when d=2?

3d + (2.d)-4

A record label surveyed 150 random visitors to its website to discover whether they prefer metal, rock, hip-hop, or jazz. The survey showed that 27 visitors preferred metal, 78 preferred rock, 21 voted for hip-hop, and 24 Liked jazz. If the company estimates sales of 3,000 copies a week at its online store, how many will likely be from the rock genre?* 520 1,500 2,100 1,560​

Jayda is watching a movie that lasts 1 hour and 37 minutes. She has watched 52 minutes so far. How many minutes are left in the movie? *

Help me I need to finish this today

You spin a spinner that is equally divided into 7 parts, and then you spin it again. 1 part is red, 2 parts are white, 3 parts are yellow and 1 part is black.
What is the probability of the spinner stopping on a white section on the first spin and then a red section on the second spin?

Hannah signs on a $148,500 mortgage at a 4.5% annual interest rate for 20 years. This results in a monthly payment is
$938.48. If only the minimum payment is made in month one, how much of the first payment goes toward reducing her
balance?
First let's find the amount of interest she paid in month 1, then find the amount toward reducing the balance.
Round to the nearest cent.

Neville is making posters for a recycling project. If each poster is a rectangle that is 12.5 inches wide and 16 inches tall, what is the perimeter of one poster?

PLEASE HELP
3/4x - 7 = 3 (1/6x +1)

Solve the linear equation and determine whether it’s one solution or infinite solution or no solution

Write the form of the partial fraction decomposition of the rational expression.
11x - 10/ (x-6)(x+7)